학술논문
Finiteness conditions for the weak commutativity group and related constructions.
Document Type
Article
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Source
Subject
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ISSN
0092-7872
Abstract
AbstractThe weak commutativity group χ(G) is generated by two isomorphic groups G and Gφ subject to the relations [g,gφ]=1 for all g∈G. We establish a finiteness criterion for the subgroups of χ(G) in terms of the set Tχ(G)={[g1,g2φ]|gi∈G}. We also obtain sufficient conditions under which some specific (local) classes of groups are invariant under the operator χ . Moreover, we prove that if G is a locally finite group with exp (G)=n, then χ(G) is locally finite and has finite n -bounded exponent.Communicated by Mark Lewis [ABSTRACT FROM AUTHOR]