We extend the notions of quasi-monomial groups and almost monomial groups, in framework supercharacter theories, we study their connection with Artin's conjecture regarding holomorphy Artin $L$-functions.

We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsion. As an outcome, we show that crossed product by in certain class preserves UCT. then quasidiagonality reduced <mml:mrow c...

Arithmetic groups are a rich class of groups where connections between topology and number theory are showcased in a particularly striking way. One construction of these groups is motivated by the modular group, PSL2(Z). The group of orientation preserving isometries of the hyperbolic upper half plane, H, is isomorphic to PSL2(R). Since Z is a discrete subgroup of R it follows that PSL2(Z) is d...

Eggert’s Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R(p) is the image of the p-th power map on R, then dimF R ≥ p dimF R(p). Whether this very elementary statement is true is not known. We examine heuristic evidence for this conjecture, versions of the conjecture that are not limited to positive characteristic ...

Let G be a finite p-group such that xZ(G) ⊆ x for all x ∈ G−Z(G), where x denotes the conjugacy class of x in G. Then |G| divides |Aut(G)|, where Aut(G) is the group of all automorphisms of G.