This article is cited in 1 paper

Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups

V. P. Burichenko

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus, Minsk, Belarus

Abstract: Let a group $\widetilde G$ be a nonsplit extension of an elementary Abelian $p$-group $V$ by the group $G=L_2(p^n)$ such that the action of $G$ on $V$ is irreducible. In the present article, we classify (up to isomorphism) such groups $\widetilde G$ with $p^n\ne3^4$.
The main part of the article consists of proofs of numerous general assertions on representations, cohomologies, and extensions of finite groups. Further, we use these results in our study of extensions by $L_2(q)$.

Key words: finite simple groups, cohomologies, nonsplit extensions.

UDC: 512.542

Received: 23.11.2012

 English version: Siberian Advances in Mathematics, 2015, 25:2, 77–109

Bibliographic databases:

•