On nilpotent groups of exponent p

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...

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...

More Fraïssé Limits of Nilpotent Groups of Finite Exponent

The class of nilpotent groups of class c and prime exponent p> c with additional predicates Pc ⊆Pc−1 ⊆ . . . ⊆P1 for suitable subgroups has the amalgamation property. Hence the Fräıssé limit D of the finite groups of this class exists. 〈1〉⊆Pc(D)⊆ . . . ⊆P2(D)⊆P1(D)=D is the lower and the upper central series of D. In this extended language, D is ultrahomogeneous. The elementary theory of D allo...

Neostability-properties of Fraïssé limits of 2-nilpotent groups of exponent p > 2

We consider the variety G2,p of nilpotent groups of class 2 of exponent p > 2 in the language L of group theory. To get the Amalgamation Property (AP) in [Bau] an additional predicate P (G) for G ∈ G2,p with G ′ ⊆ P (G) ⊆ Z(G) is introduced. Let GP2,p be the category of this groups in the extended language LP where the morphisms are embeddings. Using the class KP2,p of finite structures in GP2,...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups