Groups in which prime order elements commute

It is known that if G is a finite group in which all the elements of prime power order commute, then G is abelian. However, the same does not hold if prime power is replaced by prime. In this article, we introduce the study of a class of finite groups G in which the prime order elements commute. In particular, we discuss the relationship between these class of groups with other known classes of finite groups, like simple groups, perfect groups etc. Moreover, we also prove some results on the possible orders of such groups. Finally, we conclude with some open issues and observations supported by computational evidences using GAP.

کلیدواژه ها:

perfect group ، commuting elements ، characteristic subgroup