
A finite group is called inseparable if the only normal subgroups over which it splits are the group itself and the trivial subgroup. Let E be the formation of finite solvable groups with elementary abelian Sylow subgroups. This note establishes the fact that, up to isomorphism, there is exactly one nonnilpotent inseparable solvable group in which the E-residual is a metacyclic p-group.
Products of subgroups of abstract finite groups, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
Products of subgroups of abstract finite groups, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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