Abstract
In this paper we describe some properties of groups G that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2–3). We prove that if G is a non-solvable group that contains a solvable subgroup of index \(p^{\alpha }\) (for some prime p), then the quotient \(G/\mathsf{Rad}{(}G)\) of G over the solvable radical is asymptotically small in comparison to \(p^{\alpha }!\) (Theorem 4).
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Acknowledgements
The first author was supported by DPI/UnB and FAPDF-Brazil. The second author acknowedges the support of the CNPq projects Produtividade em Pesquisa (Project No.: 308212/2019-3) and Universal (Project No.: 21624/2018-3).
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Communicated by Adrian Constantin.
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Bastos, R., Schneider, C. Groups with a solvable subgroup of prime-power index. Monatsh Math 194, 471–480 (2021). https://doi.org/10.1007/s00605-020-01486-5
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DOI: https://doi.org/10.1007/s00605-020-01486-5