Related papers: A characterization of ZM-groups

In this short note, inspired by much recent activity centered around attempts to formulate various correspondences between the classification of affine SU(k) WZW modular-invariant partition functions and that of discrete finite subgroups of…

The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.

We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without…

For a finite group $G$, we consider the zeta function $\zeta_G(s) = \sum_{H} \abs{H}^{-s}$, where $H$ runs over the subgroups of $G$. First we give simple examples of abelian $p$-group $G$ and non-abelian $p$-group $G'$ of order $p^m, \; m…

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

The average order of a finite group G is denoted by o(G). In this note, we classify groups whose average orders are less than o(S4), where S4 is the symmetric group on four elements. Moreover, we prove that G \cong S4 if and only if o(G) =…

We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.

We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).

This abstract presents (without proofs) some new results on commutativity degree of finite groups.

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

In the first part of this note, we review results concerning analytic characterization of convexity for planar sets. The second part is devoted to results valid for arbitrary $m \ge 2$.

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

We prove Manin's conjecture for bi-equivariant compactifications of unipotent groups.

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.