Free centre-by-(abelian-by-exponent 2) groups

Free Centre-by-nilpotent-by-abelian Lie Rings

We study the free Lie ring of rank 2 in the variety of all centreby-nilpotent-by-abelian Lie rings of derived length 3. This is the quotient L/([γc(L′), L] + L′′′) with c > 2 where L is the free Lie ring of rank 2, γc(L′) is the c-th term of the lower central series of the derived ideal L′ of L, and L′′′ is the third term of the derived series of L. We show that the quotient γc(L′) + L′′′/[γc(L...

Triple factorization of non-abelian groups by two maximal subgroups

The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

Finite Quantum Groups over Abelian Groups of Prime Exponent

– 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. ...

Cotorsion theories cogenerated by א1-free abelian groups

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.

Intuitionistic Free Abelian Groups