We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.

We study the ramifications of Schur’s theorem that, if G is a group such that G/ZG is finite, then G′ is finite, if we restrict attention to nilpotent group. Here ZG is the center of G, and G′ is the commutator subgroup. We use localization methods and obtain relativized versions of the main theorems. 2000 Mathematics Subject Classification. 20B07, 20D15.

This is the rst in the series of papers dedicated to the structure of hyperbolic unitary groups over form rings and their subgroups. In this part we recall foundations of the theory and study elementary subgroup of the hyperbolic unitary group over a ring. In particular, using a variant of Suslin's patching method, we prove standard commutator formulae for relative elementary subgroups.

Twisted Alexander invariants have been defined for any knot and linear representation of its group π. The invariants are generalized for any periodic representation of the commutator subgroup π. Properties of the new twisted invariants are given. Under suitable hypotheses, reciprocality and bounds on the moduli of zeros are obtained. A topological interpretation of the Mahler measure of the inv...

A well known unresolved conjecture states that every Cayley graph on a solvable group G has a 1-factorization. We show that if the commutator subgroup of of such a group is an elementary abelian p-group, then every quartic Cayley graph on G has a 1-factorization.

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G. MSC2000: Primary 16S34, 20C05; Secondary 16U60

then we term the elements x and y n-commutative. It is not difficult to verify that »-commutativity and (1—»)-commutativity are equivalent properties of the elements x and y, that ( — ̂ -commutativity implies ordinary commutativity, and that commuting elements are »-commutative. From any concept and property involving the fact that certain elements [or functions of elements] commute, one may der...

For each simply-laced Dynkin graph ∆ we realize the simple complex Lie algebra of type ∆ as a quotient algebra of the complex degenerate composition Lie algebra L(A) 1 of a domestic canonical algebra A of type ∆ by some ideal I of L(A) 1 that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of L(A) 1 /I has a basis given by the coset o...

We give an explicit list of all p-groups G with a cyclic subgroup of index p2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also proved that such a K-basis does not exist for the group algebra KG, in the case when G is either a powerful p-group or a two generated p-group ( p 6= 2 ) with a central cyclic commutator subgroup. This p...