fa گروه‌هایی که مجموعه‌ی اعضای صفرشوی آنها اجتماع دقیقا سه کلاس تزویج است جبر alg مقاله مستقل Original Manuscript <span style="font-size:11pt"><span style="text-justify:kashida"><span style="text-kashida:0%"><span style="line-height:21.0pt"><span style="direction:rtl"><span style="unicode-bidi:embed"><span calibri="" style="font-family:"><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">فرض کنیم </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAZCAIAAABlzjOmAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAMNJREFUOE/VksENwyAMRUtnaXuoOgFM0FungHXIMrBBJqhyqNmF2hgISInCNf+AwHqy8bdFjPEyoOsAQ8jZuBC8UUpUKWUmT42gL1VgJUakdZBC4DS+paXXyhWIGRbFtKNb4Zji2JYy53Qq2ObqaeYOMa57jEWaW/h98Xw9bnXW3qzOmGQL5dtKB5Z+jI3lL+/vAdXQn3cuQtz9iZ7MC7QrBsucsBordja2gEtmdj5Vn9OMWFJbh2hnp6CZDOhs+7zX0h9l6ydpLV7pIQAAAABJRU5ErkJggg==" style="width:7.8pt; height:15pt" > </span></span></span></span></span>&nbsp;<span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">یک گروه متناهی و </span></span><m:omath><m:d><m:e><i><span dir="LTR" style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r></m:r></span></span></i></m:e></m:d></m:omath><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:31.8pt; height:15pt" > </span></span></span></span></span>&nbsp;<span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">مجموعه تمام سرشت‌های تحویل‌ناپذیر </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAZCAIAAABlzjOmAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAMNJREFUOE/VksENwyAMRUtnaXuoOgFM0FungHXIMrBBJqhyqNmF2hgISInCNf+AwHqy8bdFjPEyoOsAQ8jZuBC8UUpUKWUmT42gL1VgJUakdZBC4DS+paXXyhWIGRbFtKNb4Zji2JYy53Qq2ObqaeYOMa57jEWaW/h98Xw9bnXW3qzOmGQL5dtKB5Z+jI3lL+/vAdXQn3cuQtz9iZ7MC7QrBsucsBordja2gEtmdj5Vn9OMWFJbh2hnp6CZDOhs+7zX0h9l6ydpLV7pIQAAAABJRU5ErkJggg==" style="width:7.8pt; height:15pt" > </span></span></span></span></span><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">&nbsp;باشند. گوییم عضو </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAZCAIAAABlzjOmAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAOVJREFUOE/tk70NwjAQhW1mIRQREzgTIJpUGcFuGYKOJmkzRSrfBpkAUeDsYs7nn8RKighRcp2fvrPvvZO5tZbtqMMOxiF/bjuoL3OZQFXcV6U6AMUV+Adwb7G0xLOQ2jjB0ImJlk42caYVKEudukiIWOL8XaGZWFJSX/AxvZ+INddjckuKrC9BCJx5jYydTzMGj9vIRFnEvu1cQN17JBaNgStKHLofXAYTdGqoG5xucd2ci5bOr8vFmXEmMleYCxKZtPJK+a06MeIsOR8ocYsnjGlXSYZ94IaEny0O6DeXFf/xv/wABRIDcx2cxCsAAAAASUVORK5CYII=" style="width:7.8pt; height:15pt" > </span></span></span></span></span><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">&nbsp;در</span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAZCAIAAABlzjOmAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAMNJREFUOE/VksENwyAMRUtnaXuoOgFM0FungHXIMrBBJqhyqNmF2hgISInCNf+AwHqy8bdFjPEyoOsAQ8jZuBC8UUpUKWUmT42gL1VgJUakdZBC4DS+paXXyhWIGRbFtKNb4Zji2JYy53Qq2ObqaeYOMa57jEWaW/h98Xw9bnXW3qzOmGQL5dtKB5Z+jI3lL+/vAdXQn3cuQtz9iZ7MC7QrBsucsBordja2gEtmdj5Vn9OMWFJbh2hnp6CZDOhs+7zX0h9l6ydpLV7pIQAAAABJRU5ErkJggg==" style="width:7.8pt; height:15pt" > </span></span></span></span></span><span style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">&nbsp;یک عضو صفرشو در </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAZCAIAAABlzjOmAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAMNJREFUOE/VksENwyAMRUtnaXuoOgFM0FungHXIMrBBJqhyqNmF2hgISInCNf+AwHqy8bdFjPEyoOsAQ8jZuBC8UUpUKWUmT42gL1VgJUakdZBC4DS+paXXyhWIGRbFtKNb4Zji2JYy53Qq2ObqaeYOMa57jEWaW/h98Xw9bnXW3qzOmGQL5dtKB5Z+jI3lL+/vAdXQn3cuQtz9iZ7MC7QrBsucsBordja2gEtmdj5Vn9OMWFJbh2hnp6CZDOhs+7zX0h9l6ydpLV7pIQAAAABJRU5ErkJggg==" style="width:7.8pt; height:15pt" > </span></span></span></span></span><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">&nbsp;است اگر سرشت </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:52.8pt; height:15pt" > </span></span></span></span></span>&nbsp;<span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">موجود باشد بطوریکه </span></span><span style="font-size:11.0pt"><span style="line-height:107%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:4.0pt"><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:49.8pt; height:15pt" > </span></span></span></span></span><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">. در این مقاله، یک اثبات نسبتا</span></span><span lang="FA" style="font-size:12.0pt"><span new="" roman="" style="font-family:" times="">ﹰ</span></span><span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:"> کوتاه برای رده‌بندی</span></span> <span lang="FA" style="font-size:12.0pt"><span b="" nazanin="" style="font-family:">گروه‌های متناهی‌ای ارائه می‌دهیم که مجموعه اعضای صفرشوی آنها دقیقا اجتماع سه کلاس تزویج است.</span></span></span></span></span></span></span></span></span><br> <br> <br> &nbsp; <span style="font-size:11pt"><span style="text-justify:kashida"><span style="text-kashida:0%"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">Let </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>G</m:r></span></span></span></i></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt">&nbsp; </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">be a finite group and let</span></span></span> <m:omath><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Irr</m:r><m:r><i>(</i></m:r><m:r><i>G</i></m:r><m:r><i>)</i></m:r></span></span></span></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt">&nbsp; </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">be the set of irreducible characters of </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>G</m:r></span></span></span></i></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt"> </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">. </span></span></span><span lang="FA" style="font-size:12.0pt"><span style="line-height:115%"><span b="" nazanin="" style="font-family:">&lrm;</span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">We say that an element </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>g</m:r></span></span></span></i></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt">&nbsp; </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">in </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>G</m:r></span></span></span></i></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt">&nbsp; </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">is a vanishing element if there exists some </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>&chi;</m:r><m:r>&isin;</m:r></span></span></span></i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr> Irr</m:r><m:r><i>(</i></m:r><m:r><i>G</i></m:r><m:r><i>)</i></m:r></span></span></span></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt"> </span></span></span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">&nbsp; such that </span></span></span><m:omath><i><span style="font-size:12.0pt"><span style="line-height:115%"><span cambria="" math="" style="font-family:"><m:r>&chi;</m:r><m:r>(</m:r><m:r>g</m:r><m:r>)=0</m:r></span></span></span></i></m:omath><span style="font-size:11.0pt"><span style="line-height:115%"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:5.0pt"> </span></span></span></span></span><span lang="FA" style="font-size:12.0pt"><span style="line-height:115%"><span b="" nazanin="" style="font-family:">&lrm;</span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">. In this paper, we provide a relatively short proof for the classification of finite groups whose set of vanishing elements is the :union: of exactly three conjugacy classes</span></span></span><span lang="FA" style="font-size:12.0pt"><span style="line-height:115%"><span b="" nazanin="" style="font-family:">&lrm;</span></span></span><span style="font-size:12.0pt"><span style="line-height:115%"><span b="" mitra="" regular="" style="font-family:">.</span></span></span></span></span></span></span></span><br> <br> <br> &nbsp; کلاس‌های تزویج, سرشت های تحویل‌ناپذیر, گروه‌های حل‌پذیر, گروه فروبنیوس conjugacy classes, irreducible characters, solvable groups, Frobenius groups, vanishing elements. 70 79 http://mmr.khu.ac.ir/browse.php?a_code=A-10-787-5&slc_lang=fa&sid=1 Sajjad Mahmood Robati سجاد محمود رباطی sajjad.robati@gmail.com 10031947532846006403 10031947532846006403 Yes دانشگاه بین المللی امام خمینی