Publication

Untitled

Ellis, Graham
Identifiers
http://hdl.handle.net/10379/9117
 https://doi.org/10.13025/23509
Publication Date
2001-10-01
Keywords
tensor-products, finite-groups
Type
Article
Downloads
Show all metadata
Citation
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.
Funder
Publisher
American Mathematical Society (AMS)
Publisher DOI
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
Collections
Externally hosted open access publications with University of Galway authors (1)