On some sufficient conditions of supersolvability of finite groups
Copyright policy )On some sufficient conditions of supersolvability of finite groups
A subgroup \(H\) of a group \(G\) is called \(c\)-supplemented if there exists a subgroup \(K\) of \(G\) such that \(G=HK\) and \(H\cap K\leq H_G\). In this paper, among other results, the authors prove that if a finite group \(G\) contains a quaternion-free normal subgroup \(N\) such that \(G/N\) is supersoluble and every subgroup of prime order of \(N\) is \(c\)-supplemented in \(G\), then \(G\) is supersoluble.
generalized Fitting subgroup, Products of subgroups of abstract finite groups, Special subgroups (Frattini, Fitting, etc.), Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, formations, \(c\)-supplemented subgroups, supersolvable groups, minimal subgroups
generalized Fitting subgroup, Products of subgroups of abstract finite groups, Special subgroups (Frattini, Fitting, etc.), Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, formations, \(c\)-supplemented subgroups, supersolvable groups, minimal subgroups
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