Finite groups with 2-nilpotent subgroups of even index
Copyright policy )Finite groups with 2-nilpotent subgroups of even index
Let \(G\) be a finite group such that every subgroup of even index whose order is divisible by at most two distinct primes has a normal 2-complement. The author gives the exact structure of \(G/O(G)\). In particular, he proves that every non-abelian composition factor of \(G\) is isomorphic either to \(L_2(q\)), \(q=8r\pm 3\), or to \(L_2(2^p)\), \(p\) a prime.
Frobenius groups, Products of subgroups of abstract finite groups, biprimary subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Shmidt groups, Finite simple groups and their classification, normal complements, composition factors, finite groups
Frobenius groups, Products of subgroups of abstract finite groups, biprimary subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Shmidt groups, Finite simple groups and their classification, normal complements, composition factors, finite groups
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