Groups with finitely many normalizers of infinite index
Groups with finitely many normalizers of infinite index
The authors study groups in which only finitely many normalizers of (infinite) subgroups have infinite index. The main results are the following theorems. Theorem A. Let \(G\) be a group in which all but finitely many normalizers of Abelian subgroups have finite index. Then the factor group \(G/Z(G)\) is finite. Theorem B. Let \(G\) be a locally finite group in which all but finitely many normalizers of infinite subgroups have finite index. Then either \(G\) is a Chernikov group or \(G/Z(G)\) is finite. Theorem C. Let \(G\) be a non-periodic group in which all but finitely many normalizers of infinite subgroups have finite index, if \(G\) contains an infinite periodic subgroup, then the factor group \(G/Z(G)\) is finite.
normalizer subgroups, normalizers of infinite index, General structure theorems for groups, almost normal subgroups, finitely many conjugates, FC-groups and their generalizations, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, subnormal subgroups
normalizer subgroups, normalizers of infinite index, General structure theorems for groups, almost normal subgroups, finitely many conjugates, FC-groups and their generalizations, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, subnormal subgroups
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