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Finite groups with some CAP-subgroups

Author

Listed:
  • Jianjun Liu

    (Shanghai University)

  • Shirong Li

    (Guangxi University)

  • Zhengcai Shen

    (Suzhou University)

  • Xiaochun Liu

    (Guangxi University)

Abstract

Let G be a finite group. A subgroup H of G is called a CAP-subgroup if the following condition is satisfied: for each chief factor K/L of G either HK = HL or H ∩ K = H ∩ L. Let p be a prime factor of |G| and let P be a Sylow p-subgroup of G. If d is the minimum number of generators of P then there exists a family of maximal subgroups of P, denoted by M d (P)={P 1, P 2,…, P d } such that ∩ i=1 d P i = ϕ(P). In this paper, we investigate the group G satisfying the condition: every member of a fixed M d (P) is a CAP-subgroup of G. For example, if, in addition, G is p-solvable, then G is p-supersolvable.

Suggested Citation

  • Jianjun Liu & Shirong Li & Zhengcai Shen & Xiaochun Liu, 2011. "Finite groups with some CAP-subgroups," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(3), pages 145-156, June.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:3:d:10.1007_s13226-011-0009-5
    DOI: 10.1007/s13226-011-0009-5
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