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 Mat. Tr., 2014, Volume 17, Number 1, Pages 19–69 (Mi mt266)

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.

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

Bibliographic databases:

Document Type: Article
UDC: 512.542

Citation: V. P. Burichenko, “Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups”, Mat. Tr., 17:1 (2014), 19–69; Siberian Adv. Math., 25:2 (2015), 77–109

Citation in format AMSBIB
\Bibitem{Bur14} \by V.~P.~Burichenko \paper Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups \jour Mat. Tr. \yr 2014 \vol 17 \issue 1 \pages 19--69 \mathnet{http://mi.mathnet.ru/mt266} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236360} \transl \jour Siberian Adv. Math. \yr 2015 \vol 25 \issue 2 \pages 77--109 \crossref{https://doi.org/10.3103/S1055134415020017}