相关论文: On Groups with a Supercomplemented Subgroup

Consideration of certain properties of group rings and their ideals search

We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…

In this note, we study the problem on the existence of non-cyclic free subgroups of the skew group algebra of a locally finite group over a field.

A subgroup $H$ of a finite group $G$ is said to be an $\mathscr{H}C$-subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^g \cap N_T(H)\leq H$ for all $g\in G$. In this paper, we investigate the structure of…

In this paper it is shown that every finite cyclic group satisfies the CI-property for the class of balanced configurations.

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite…

In what follows we generalize the notion of a complemented ring to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.

A subgroup $H$ of a group $G$ is called weakly s-supplemented in $G$ if there is a subgroup $T$ such that $G=HT$ and $H\cap T\le H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are s-permutable…

In this note we study the finite groups whose subgroup lattices are dismantlable.

We consider some applications of the theory of generalized Ore supplement conditions in the study of finite groups.

Marius T\u{a}rn\u{a}uceanu described the finite groups $G$ having $|G|-1$ cyclic subgroups. We describe the finite groups $G$ having $|G|-\Delta$ cyclic subgroups for $\Delta=2, 3, 4$ and $5$.

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

We prove that each infinite 2-group with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group or to the infinite group of generalized quaternions.

In this paper we study probabilistic aspects such as subgroup commutativity degree and cyclic subgroup commutativity degree of the (generalized) dicyclic groups. We find explicit formulas for these concepts and we provide another example of…

Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G…

By a covering of a group G we mean an epimorphism from a group F to G. Introducing the notion of strong covering as a covering pi:F-->G such that every automorphism of G is a projection via pi of an automorphism of F, the main aim of this…

We classify those 2-groups G which factorise as a product of two disjoint cyclic subgroups A and B, transposed by an automorphism of order 2. The case where G is metacyclic having been dealt with elsewhere, we show that for each e>2 there…

We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.