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,...

The theory of alternating bilinear forms on finite dimensional vector spaces V is well understood; two forms on V are equivalent if and only if they have equal ranks. The situation for alternating trilinear forms is much harder. This is partly because the number of forms of a given dimension is not independent of the underlying field and so there is no useful canonical description of an alterna...

This paper studies the MOR cryptosystem, using the auto-morphism group of the extra-special p-group of exponent p, for an odd prime p. Similar results can be obtained for extra-special p-groups of exponent p 2 and for the even prime.

– We classify pointed finite-dimensional complex Hopf algebras whose group of group-like elements is abelian of prime exponent p, p > 17. The Hopf algebras we find are members of a general family of pointed Hopf algebras we construct from Dynkin diagrams. As special cases of our construction we obtain all the Frobenius–Lusztig kernels of semisimple Lie algebras and their parabolic subalgebras. ...