Some abelian-by-nilpotent varieties of p-groups

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

Character Varieties of Abelian Groups

We prove that for every reductive group G with a maximal torus T and Weyl group W there is a natural normalization map χ from T/W to an irreducible component, X 0 G(Z ), of the G-character variety XG(Z ) of Z . We prove that this component is reduced and that χ is an isomorphism for classical groups. Additionally, we prove that even though there are no irreducible representations of Z into redu...

some inequalities for nilpotent multipliers of powerful p-groups

Some Abelian Varieties with Visible Shafarevich-Tate Groups

We give examples of abelian variety quotients of the modular jacobian J0(N) with nontrivial visible Shafarevich-Tate groups. In computing these examples we developed formulas for invariants of higher dimensional modular abelian varieties.

Fitting quotients of finitely presented abelian-by-nilpotent groups

We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.