A characterization of finite -soluble -groups

  • Chenchen Cao

    Ningbo University, China
  • Dein Wong

    China University of Mining and Technology, Xuzhou, China
  • Chi Zhang

    China University of Mining and Technology, Xuzhou, China
A characterization of finite $\sigma$-soluble $P\sigma T$-groups cover

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Abstract

Let be a non-empty class of groups, a finite group and be the lattice of all subgroups of . A chief factor of is -central in if . Let be the set of subgroups of such that every chief factor of between and is -central in ; let be the set of subgroups of such that . In this paper, we study the influence of and on the structure of , where is a normally hereditary saturated formation containing all -nilpotent groups and is -soluble. Moreover, we give a new characterization of a finite -soluble group to be a -group.

Cite this article

Chenchen Cao, Dein Wong, Chi Zhang, A characterization of finite -soluble -groups. Rend. Sem. Mat. Univ. Padova 148 (2022), pp. 203–212

DOI 10.4171/RSMUP/108