
Assume H H and H 0 {H_0} are subgroups of the finite group G G with H 0 ⧋ H H_0 \triangleubar H . Three theorems are presented which give criteria for the existence of a relative normal complement in G G of H H over H 0 {H_0} .
pi-subgroups, Products of subgroups of abstract finite groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, existence of relative normal complement, Series and lattices of subgroups
pi-subgroups, Products of subgroups of abstract finite groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, existence of relative normal complement, Series and lattices of subgroups
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