Related papers: A sufficient condition for accessibility of pro-$p…

We propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…

We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.

We determine a reasonable upper bound for the complexity of collection from the left to multiply two elements of a finite soluble, or polycyclic, group by restricting attention to certain polycyclic presentations of the group.

Let $G$ be a finitely generated group. We prove that the $n$-fold tensor product $G^{\otimes n}$ is finite (resp. polycyclic) if and only $G$ is finite (resp. polycyclic). Further, assuming that $G$ is finitely presented, we show that…

We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be…

This paper is dedicated to the problem of infinite transitivity for algebraically generated automorphism groups of the affine plane. We provide a necessary and sufficient condition of infinite transitivity for a large family of subgroups…

Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category…

In [10] Benjamin Klopsch and Ilir Snopce posted the conjecture that for $p\geq 3$ and $G$ a torsion-free pro-$p$ group $d(G)=\dim (G)$ is a sufficient and necessary condition for the pro-$p$ group $G$ to be uniform. They pointed out that…

In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.

We prove that the cut space of any transitive graph $G$ is a finitely generated ${\rm Aut}(G)$-module if the same is true for its cycle space. This confirms a conjecture of Diestel which says that every locally finite transitive graph whose…

We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor…

Let p: Y--> X be a surjection between schemes projective over the algebraic closure of a finite field. Let L be a line bundle on X such that p^*(L) is globally generated. I give a natural necessary and sufficient condition under which some…