Related papers: Integral group rings with all central units trivia…

In this note, we study the finite groups with the number of cylic subgroups no greater than 6.

In this paper, we provide new criteria for the solvability and supersolvability of a finite group based on its number of cyclic subgroups. A finite group G is called n-cyclic if it contains n cyclic subgroups. This paper also partially…

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there…

The Subgroup Isomorphism Problem for Integral Group Rings asks for which finite groups U it is true that if U is isomorphic to a subgroup of V(ZG), the group of normalized units of the integral group ring of the finite group G, it must be…

We prove that the only separable commutative ring-objects in the stable module category of a finite cyclic p-group G are the ones corresponding to subgroups of G. We also describe the tensor-closure of the Kelly radical of the module…

In the first section of the paper, we will give some basic definitions and properties about Crystalline Graded Rings. In the following section we will provide a general description of the center. Afterwards, the case where the grading group…

Let $F$ be a field of characteristic $p > 0$. We study the structure of the finite groups $G$ for which the socle of the center of $FG$ is an ideal in $FG$ and classify the finite $p$-groups $G$ with this property. Moreover, we give an…

In this paper, we give the definition of {\em weakly locally finite} division rings and we show that the class of these rings strictly contains the class of locally finite division rings. Further, we study multiplicative subgroups in these…

What are all rings $R$ for which $R^*$ (the group of invertible elements of $R$ under multiplication) is an elementary abelian $p$-group? We answer this question for finite-dimensional commutative $k$-algebras, finite commutative rings,…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We describe the main questions connected to torsion subgroups in the unit group of integral group rings of finite groups and algorithmic methods to attack these questions. We then prove the Zassenhaus Conjecture for Amitsur groups and prove…

This note proves a generalisation to inverse semigroups of Anisimov's theorem that a group has regular word problem if and only if it is finite, answering a question of Stuart Margolis. The notion of word problem used is the two-tape word…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

Suppose that $G$ is a finite solvable group and $V$ is a finite, faithful and completely reducible $G$-module. Let $N$ be a nilpotent subgroup of $G$, then there exits $v \in V$ such that $|\bC_N(v)| \leq (|N|/p)^{1/p}$, where $p$ is the…

Let $p$ be a prime integer and $\mathbb{Z}_p$ be the ring of $p$-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group ${\rm…

In this note, a necessary and sufficient condition for the normalizer of a core-free subgroup $H$ of a finite group $G$ to be normal in $G$ is obtained. Also, a known result of finite groups is obtained through transversal.

There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or…

Given a surjective ring homomorphism, we study when the induced group homomorphism on unit groups is surjective. To this end, we introduce notions of generalized inverses and units, as well as a class of rings such that the set of closed…

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…