Number of Compatible Pair of Actions for Finite Cyclic Groups of P-Power Order

Abstract

The compatible actions played an important role before determining the nonabelian tensor product of groups. Different compatible pair of actions gives a different nonabelian tensor product even for the same group. The aim of this paper is to determine the exact number of the compatible pair of actions for the finite cyclic groups of p-power order where p is an odd prime. By using the necessary and sufficient number theoretical conditions for a pair of the actions to be compatible with the actions that have p-power order, the exact number of the compatible pair of actions for the finite cyclic groups of p-power order has been determined and given as a main result in this paper.

The compatible action graphs for finite cyclic 2-groups

“…In [6] continues the studies on compatible pair of nontrivial action for finite cyclic 2-groups. After that, in [7] studies on compatible number of compatible pair of action for finite cyclic groups of p-power order.…”