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On the relation between upper central quotients and lower central series of a group

Ellis, Graham
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http://hdl.handle.net/10379/9117
 https://doi.org/10.13025/23509
Publication Date
2001-10-01
Keywords
Externally hosted open access publications with University of Galway authors, finite-groups
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journal article
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Ellis, Graham (2001). . Transactions of the American Mathematical Society 353 (10), 4219-4234
Abstract
Let H be a group with a normal subgroup N contained in the upper central subgroup Z(c)H. In this article we study the influence of the quotient group G = H/N on the lower central subgroup gamma Hc+1. In particular, for any finite group G we give bounds on the order and exponent of gamma Hc+1. For G equal to a dihedral group, or quaternion group, or extra-special group we list all possible groups that can arise as gamma Hc+1. Our proofs involve: (i) the Baer invariants of G, (ii) the Schur multiplier M (L,G) of G relative to a normal subgroup L, and (iii) the nonabelian tensor product of groups. Some results on the nonabelian tensor product may be of independent interest.
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American Mathematical Society (AMS)
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