JournalsrsmupVol. 135pp. 195–206

Characterizations of hypercyclically embedded subgroups of finite groups

  • Xiaolan Yi

    Zhejiang University of Science and Technology, Hangzhou, China
Characterizations of hypercyclically embedded subgroups of finite groups cover
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Abstract

A normal subgroup HH of a finite group GG is said to be hypercyclically embedded in GG if every chief factor of GG below HH is cyclic. Our main goal here is to give new characterizations of hypercyclically embedded subgroups. In particular, we prove that a normal subgroup EE of a finite group GG is hypercyclically embedded in GG if and only if for every different primes pp and qq and every pp-element a(GF(E))Ea \in (G' \cap F^{*}(E))E', pp'-element bGb \in G and qq-element cGc \in G' we have [a,bp1]=1=[aq1,c][a, b^{p-1}]=1=[a^{q-1}, c]. Some known results are generalized. \end{abstract}

Cite this article

Xiaolan Yi, Characterizations of hypercyclically embedded subgroups of finite groups. Rend. Sem. Mat. Univ. Padova 135 (2016), pp. 195–206

DOI 10.4171/RSMUP/135-11