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 ∩ d i=1 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.
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Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi autonomous region (No. 0249001).
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Liu, J., Li, S., Shen, Z. et al. Finite groups with some CAP-subgroups. Indian J Pure Appl Math 42, 145–156 (2011). https://doi.org/10.1007/s13226-011-0009-5
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DOI: https://doi.org/10.1007/s13226-011-0009-5