8 research outputs found
Minimal odd order automorphism groups
We show that 3^7 is the smallest order of a non-trivial odd order group which
occurs as the full automorphism group of a finite group.Comment: 11 pages, no figures. Manuscript accepted for publicatio
Counting commutativities in finite algebraic systems
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
Counting commutativities in finite algebraic systems
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