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- A. A new recognition of some finite simple groups. mmr 2023; 9 (1) :108-118

URL: http://mmr.khu.ac.ir/article-1-3166-en.html

URL: http://mmr.khu.ac.ir/article-1-3166-en.html

In this paper G is considered to be a finite group. We denote the set of elements order and the set of prime divisors of order G by

Let G be a group with the Steinberg group

In this research we prove that Steinberg group

In this section we prove the main result of this article. For simplicity the Steinberg simple group and prime number are denoted by D and p respectively. As mentioned in the previous section to prove the main result of this article we use the Lemma 4.2 of [18]. We prove p is an isolated vertex of prime graph. Using Lemma 4.2 we prove that G neither a Frobenius nor 2-Frobenius group. And for the case c this Lemma is satisfied. In other words, G has a normal series such that H and G/K and K/H are non-abelian simple groups. Moreover, H is a nilpotent group. Every odd components of prime is an odd component of the prime graph. In the next step, by using Lemma 7.2, since (5, ∣G∣)=1, we consider the groups of this Lemma. We also prove that isomorphism K/H

We conclude that in addition to a previously known criterion(test) for Steinberg groups recognition by their 2-sylow subgroups(ANTHONY HUGHES, CHARACTERIZATION OF

Type of Study: Research Paper |
Subject:
Mat

Received: 2021/01/18 | Revised: 2024/01/7 | Accepted: 2021/06/22 | Published: 2023/06/20 | ePublished: 2023/06/20

Received: 2021/01/18 | Revised: 2024/01/7 | Accepted: 2021/06/22 | Published: 2023/06/20 | ePublished: 2023/06/20

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