On some ranks of infinite groups |
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| Authors: | Martyn R. Dixon Leonid A. Kurdachenko Nikolay V. Polyakov |
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| Affiliation: | (1) Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.;(2) Department of Algebra, University of Dnepropetrovsk, Vulycya Naukova 13, Dnepropetrovsk 50, 49050, Ukraine;(3) President, National Dnepropetrovsk University, Vulycya Naukova 13, Dnepropetrovsk 50, 49050, Ukraine |
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| Abstract: | Abstract A group G has finite Hirsch-Zaicev rank rhz(G) = r if G has an ascending series whose factors are either infinite cyclic or periodic and if the number of infinite cyclic factors is exactly r. The authors discuss groups with finite Hirsch-Zaicev rank and the connection between this and groups having finite section p-rank for some prime p, or p=0. Groups all of whose abelian subgroups are of bounded rank are also discussed. Keywords: p-rank, locally generalized radical group, Hirsch-Zaicev rank, torsion-free rank, rank Mathematics Subject Classification (2000): 20F19, 20E25, 20E15 |
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