Finite and locally solvable periodic groups with given intersection of certain subgroups
Finite and locally solvable periodic groups with given intersection of certain subgroups
Let \(p\) be a prime. A group \(G\) is an \(IC_p\)-group if for any finite subgroups \(H\) and \(K\) of \(G\) such that \(H\nleq K\) and \(K\nleq H\), a Sylow \(p\)-subgroup of \(H\cap K\) is cyclic. The authors completely classify finite soluble \(IC_p\)-groups and periodic locally soluble \(IC_p\)-groups.
finite subgroups, finite soluble groups, locally soluble groups, Sylow subgroups, Generalizations of solvable and nilpotent groups, Solvable groups, supersolvable groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, periodic groups, Local properties of groups, 510
finite subgroups, finite soluble groups, locally soluble groups, Sylow subgroups, Generalizations of solvable and nilpotent groups, Solvable groups, supersolvable groups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, periodic groups, Local properties of groups, 510
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