Finite p-groups of exponent p2 in which each element commutes with its endomorphic images

COMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2

The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...

FINITE NONABELIAN p-GROUPS OF EXPONENT > p WITH A SMALL NUMBER OF MAXIMAL ABELIAN SUBGROUPS OF EXPONENT > p

Y. Berkovich has proposed to classify nonabelian finite pgroups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case

THE NILPOTENCY CLASS OF FINITE GROUPS OF EXPONENT p

We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of ...

On the Exponent of Triple Tensor Product of p-Groups

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

Finite Groups with p-Sylow Coverings