GROUP PARTITIONS VIA COMMUTATIVITY

Authors : A MAHMOUDİFAR, A R MOGHADDAMFAR, F SALEHZADEH

Pages : 224-231

Doi:10.24330/ieja.504159

View : 17 | Download : 7

Publication Date : 2019-01-08

Article Type : Research Paper

Abstract :Let $G$ be a nonabelian group, $A\subset G$ an abelian subgroup and $n\geqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into  $A$ and $n$ disjoint commuting subsets $A_1,  A_2,\ldots, A_n$ of $G$,  such that $|A_i|>1$ for each $i=1, 2, \ldots, n$. We classify all nonabelian groups, up to isomorphism,  which have an $n$-abelian partition, for $n=2$ and $3$.
Keywords : n Abelian partition, commuting graph