On II-properties of Finite Groups |
Common terms and phrases
Abelian ai+1 arbitrary element ascending central series assertion assumption characteristic subgroup commutes composition factors composition series condition Consider the normalizer contains contradiction definition divide the order divis divisible by q element of order exist groups finite group fore group is insoluble group of order group of smallest groups whose order Hence it follows highest power isomorphic least one soluble lemma less than g low-regular N₁ N₂ nilpotent groups normal sub normal subgroup number with respect numbers P1 obtain obviously order g order not divisible order P1 p-Abelian group p-commutator p-decomposable groups p-derived group p-nilpotent p-soluble p-Sylow p-Sylow-subgroup pd-group prime divisor principal series S. A. Čunihin satisfies series of normal smallest order soluble and conjugate soluble with respect subgroup of order supersoluble with respect Sylow's theorem t₁ Theo theorem holds Theorem III theorem is false theorem of Burnside theorem of Sylow Theorem XVII