On solvability of finite groups with some ss-supplemented subgroups

Abstract

On solvability of finite groups with some ss-supplemented subgroups Czechoslovak Mathematical Journal, Vol. 65 (2015) Abstract. A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is s-permutable in K. In this paper, we first give an example to show that the conjecture in A. A. Heliel's paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature.

Finite groups with some SS-supplemented subgroups

“…The research on the SS-supplemented subgroups of a given group still continues and many related results have been recently obtained, see [11], [12]. It has been proved that the SS-supplemented subgroups are suitable for describing the structure of groups.…”