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Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. There is a set Md(P ) = {P1, P2, · · · , Pd} of maximal subgroups of P such that ⋂d i=1 Pi = Φ(P ). In the present paper, we investigate the structure of a finite group under the assumption that every member ofMd(P ) is either s-permutably embedded or weakly s-permutable in G to give criteria for a group to be p-supersolvable or p-nilpotent.

confluentes mathematici

Finite Groups with some <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math>-Permutably Embedded and Weakly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math>-Permutable Subgroups

Finite Groups with some s-Permutably Embedded and Weakly s-Permutable Subgroups