On Factor Groups of some Groups

zbMATH Open1265.20039arXiv1111.3128MaRDI QIDQ4899470

N. S. Chernikov

Publication date: 8 January 2013

Abstract: Let for a prime $p$, $mathfrakX$ (respectively $mathfrakY$) be the class of all $p$-biprimitively finite (respectively periodic $p$-conjugatively biprimitively finite) groups and $GinmathfrakX$ (respectively $GinmathfrakY$), $V$ be a periodic subgroup of $G$ having an ascending series of normal in $G$ subgroups such that each its factor is an almost layer-finite group or a locally graded group of finite special rank, or a $WF$-group with $min-q$ on all primes $q$. We prove that $G/VinmathfrakX$ (respectively $G/VinmathfrakY$). Also some interesting and useful preliminary results are obtained.

Full work available at URL: https://arxiv.org/abs/1111.3128

zbMATH Keywords

periodic groupslocally graded groupsperiodic subgroupsfactor groupsconjugately biprimitively finite groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Other classes of groups defined by subgroup chains (20F22) Chains and lattices of subgroups, subnormal subgroups (20E15) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25)

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