Abstract We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

We determine the automorphism group of the split Cartan modular curves Xsplit(p) for all primes p.

We give several algorithms for finitely generated subgroups of the modular group PSL2(Z), given by sets of generators. First, we present an algorithm to check whether a finitely generated subgroup H has finite index in the full modular group. Then we discuss how to parametrise the right cosets of H in PSL2(Z), whether the index is finite or not. Further, we explain how an element in H can be wr...

We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent then its upper (or lower) Lie nilpotency index is at most |G| + 1, where |G| is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal have already been determined. Here we determine G for which upper (or lower) L...

Let p be a prime, G a locally finite p -group, K a commutative ring of characteristic p . The anti-automorphism g 7→ g of G extends linearly to an anti-automorphism a 7→ a∗ of KG . An element a of KG is called symmetric if a∗ = a . In this paper we answer the question: for which G and K do the symmetric units of KG form a multiplicative group. Let G be a group, K a commutative ring (with 1), an...