$On periodic groups isospectral to $A_7$$

On periodic groups isospectral to $A_7$

The spectrum of a periodic group $G$ is the set $\omega(G)$ of its element orders. Consider a group $G$ such that $\omega(G)=\omega(A_7)$. Assume that $G$ has a subgroup $H$ isomorphic to $A_4$, whose involutions are squares of elements of order $4$. We prove that either \(O_2(H) \su...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2018-10
1. Verfasser:	Mamontov, Andrey
Format:	Artikel
Sprache:	eng
Schlagworte:	Subgroups
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	The spectrum of a periodic group $G$ is the set $\omega(G)$ of its element orders. Consider a group $G$ such that $\omega(G)=\omega(A_7)$. Assume that $G$ has a subgroup $H$ isomorphic to $A_4$, whose involutions are squares of elements of order $4$. We prove that either $O_2(H) \subseteq O_2(G)$ or $G$ has a finite nonabelian simple subgroup.
ISSN:	2331-8422

Zusammenfassung:	The spectrum of a periodic group \(G\) is the set \(\omega(G)\) of its element orders. Consider a group \(G\) such that \(\omega(G)=\omega(A_7)\). Assume that \(G\) has a subgroup \(H\) isomorphic to \(A_4\), whose involutions are squares of elements of order \(4\). We prove that either \(O_2(H) \subseteq O_2(G)\) or \(G\) has a finite nonabelian simple subgroup.
ISSN:	2331-8422

On periodic groups isospectral to \(A_7\)