Counting commutativities in finite algebraic systems
Irish Mathematical Society
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.
Commutative algebra , Semigroups (Algebra) , Ring theory , Commutativities , Groups
Dolan, B., MacHale, D. and MacHale, P. (2016) 'Counting Commutativities in Finite Algebraic Systems', Bulletin of the Irish Mathematical Society, 77, pp. 61-70.
© 2016 Irish Mathematical Society