Counting commutativities in finite algebraic systems

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Date
2016
Authors
Dolan, Brian
MacHale, Desmond
MacHale, Peter
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Publisher
Irish Mathematical Society
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Abstract
We examine the total possible number of commutativities in a finite algebraic system, concentrating on groups, but also examining rings and semigroups. Numerical restrictions are found and bounds for the total number of commutativities in subgroups and factor groups are derived. Finally, a curious connection with group representations is explored.
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Keywords
Commutative algebra , Semigroups (Algebra) , Ring theory , Commutativities , Groups
Citation
Dolan, B., MacHale, D. and MacHale, P. (2016) 'Counting Commutativities in Finite Algebraic Systems', Bulletin of the Irish Mathematical Society, 77, pp. 61-70.
Link to publisher’s version
http://banach.ucd.ie/bull77/index.php
URI
https://hdl.handle.net/10468/9600
Collections
Mathematical Sciences- Journal Articles
Copyright
© 2016 Irish Mathematical Society