|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
A New Characterization of Sporadic Groups | | Zhongbi Wang
; Heng Lv
; Yanxiong Yan
; Guiyun Chen
; | | Date: |
16 Sep 2020 | | Abstract: | Let $G$ be a finite group, $n$ a positive integer. $pi(n)$ denotes the set
of all prime divisors of $n$ and $pi(G)=pi(|G|)$. The prime graph $Gamma(G)$
of $G$, defined by Grenberg and Kegel, is a graph whose vertex set is $pi(G)$,
two vertices $p, q$ in $pi(G)$ joined by an edge if and only if $G$ contains
an element of order $pq$. In this article, a new characterization of sporadic
simple groups is obtained, that is, if $G$ is a finite group and $S$ a sporadic
simple group. Then $Gcong S$ if and only if $|G|=|S|$ and $Gamma(G)$ is
disconnected. This characterization unifies the several characterizations that
can conclude the group has non-connected prime graphs, hence several known
characterizations of sporadic simple groups become the corollaries of this new
characterization. | | Source: | arXiv, 2009.07490 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER