Define a module representation to be a linear parameterisation of a collection of module
homomorphisms over a ring. Generalising work of Knuth, we define duality functors indexed …

We show that the enumeration of linear orbits and conjugacy classes of $\mathbf {Z} $-
defined unipotent groups over finite fields is “wild” in the following sense: given an arbitrary …

We present a new algorithm to decide isomorphism between finite graded algebras. For a
broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the …

We describe the automorphism groups of finite p-groups arising naturally via Hessian
determinantal representations of elliptic curves defined over number fields. Moreover, we …

We produce a long exact sequence whose terms are unit groups of associative algebras that
behave as inner automorphisms of a given tensor. Our sequence generalizes known …

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients
in a field $ K $, whose determinant describes a smooth cubic in the projective plane. To …

Within a category $\mathtt {C} $, having objects $\mathtt {C} _0 $, it may be instructive to
know not only that two objects are non-isomorphic, but also how far from being isomorphic …

Let p be an odd prime and let G be a non-abelian finite p-group of exponent p2 with three
distinct characteristic subgroups, namely 1, Gp and G. The quotient group G/Gp gives rise to …

For a finite group GG, let σ (G) σ(G) be the number of subgroups of GG and σ ι (G) σ_ι(G) the
number of isomorphism types of subgroups of G G. Let L= L r (pe) L=L_r(p^e) denote a …

We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the
Lie algebra of derivations of a tensor to compress the space in which the search takes place …