Groups with large centralizer subgroups
Groups with large centralizer subgroups
Let \(C_G(X)\) denote the centralizer of a subgroup \(X\) of a group \(G\). A subgroup \(X\) of \(G\) is called self-centralizing in \(G\) if \(C_G(X)\leq X\). The paper is concerned with groups in which the set of non-Abelian self-centralizing subgroups is small in some sense. Certainly every proper subgroup of a Tarski group is self-centralizing. Various nice results are proved. For example, if \(G\) is a locally graded group with only finitely many self-centralizing non-Abelian subgroups then \(G/Z(G)\) is finite, where \(Z(G)\) is the centre of \(G\).
self-centralizing subgroups, FC-groups and their generalizations, Generalizations of solvable and nilpotent groups, metahamiltonian groups, metahamiltonian group; self-centralizing subgroup, Subgroup theorems; subgroup growth, locally graded groups, 510
self-centralizing subgroups, FC-groups and their generalizations, Generalizations of solvable and nilpotent groups, metahamiltonian groups, metahamiltonian group; self-centralizing subgroup, Subgroup theorems; subgroup growth, locally graded groups, 510
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!