On partially τ-quasinormal subgroups of finite groups

Year 2014, Volume: 43 Issue: 6, 953 - 961, 01.12.2014

Changwen Li Xuemei Zhang Xiaolan Yi

Abstract

Let H be a subgroup of a group G. We say that: (1) H is τ -quasinormal
in G if H permutes with every Sylow subgroup Q of G such that
(|H|, |Q|) = 1 and (|H|, |Q
G|) 6= 1; (2) H is partially τ -quasinormal
in G if G has a normal subgroup T such that HT is S-quasinormal
in G and H ∩ T ≤ HτG, where HτG is the subgroup generated by all
those subgroups of H which are τ -quasinormal in G. In this paper,
we find a condition under which every chief factor of G below a normal
subgroup E of G is cyclic by using the partial τ -quasinormality of some
subgroups.

Keywords

S-quasinormal, partially τ -quasinormal, cyclic

References

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