The genus of the product of a group with an Abelian group
type: Item
instance of: scholarly article
title: The genus of the product of a group with an Abelian group
zbMATH Open document ID: 0683.05025
DOI: 10.1016/S0195-6698(89)80021-6
author: Tomaž Pisanski
author: Thomas W. Tucker
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: The genus \(\gamma\) (G) of a group G is the minimum genus of any orientable surface containing an embedding of some Cayley graph for G. The genus of the direct product \(G\times A\) of an arbitrary finite group G and a finite abelian group A is determined for many G and most abelian groups A of sufficiently large rank. The authors present sufficient conditions on the groups G and A such that \(\gamma (G\times A)=1+| G\times A| (r-2)/4,\) where r is the rank of A, \(r>3\), and A has no factors \({\mathbb{Z}}_ 2\) and \({\mathbb{Z}}_ 3\) in its canonical form.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 4118397
zbMATH Keywords: genus
zbMATH Keywords: group
zbMATH Keywords: Cayley graph
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
cites work: Q5577154
cites work: On finite simple groups of characteristic 2 type
cites work: Q3757929
cites work: On the genus of finite abelian groups
cites work: Universal commutator graphs
cites work: The genus of low rank Hamiltonian groups
cites work: Nonorientable embeddings of groups
cites work: Q4156452
full work available at URL: s0195-6698(89)80021-6
OpenAlex ID: W2029376260
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description: scientific article; zbMATH DE number 4118397