Related papers: Strongly closed subgroups of finite groups

We describe finite soluble groups in which every $n$-maximal subgroup is $\mathfrak F$-subnormal.

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classification of finite metahamiltonian $p$-groups is given.

One of the aims of this paper is to obtain structural results showing that powerful subgroups are abundant in pro-$p$ groups admitting certain powerful quotients. In particular, we obtain an analogue of Baer's theorem for powerful pro-$p$…

In this paper we complete the description of the $B\mathbb{Z} /p$-cellularization of the classifying spaces of all finite groups, for all primes $p$. The techniques are based in a careful analysis of the $p$-fusion structure of the groups…

In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.

It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are…

Finite $p$-groups with a unique $\mathcal{A}_2$-subgroup are classified up to isomorphism. A problem proposed by Berkovich and Janko is solved.

In this paper, we proved that a group $G$ is supersoluble if and only if for any prime $p\in \pi (G)$ there exists a supersoluble subgroup of index $p$.

We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$.

We establish conditions under which the fundamental group of a graph of finite $p$-groups is necessarily residually $p$-finite. The technique of proof is independent of previously established results of this type, and the result is also…

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.

In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

This work gives a classification of imprimitive irreducible finite subgroups of the orthogonal group O(7) plus the number of conjugate classes for each group.

In this note we describe the finite groups $G$ having $|G|-2$ cyclic subgroups. This partially solves the open problem in the end of \cite{3}.

We determine the closure of a cyclic subgroup $H$ of a free group for the pro-{\bf V} topology when {\bf V} is an extension-closed pseudovariety of finite groups. We show that $H$ is always closed for the pro-nilpotent topology and compute…

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.

We classify all finite $p$-groups $G$ for which |$Aut_{c}(G)$| attains its maximum value, where $Aut_{c}(G)$ denotes the group of all class preserving automorphisms of $G$ .

Suppose $C(G)$ denotes the set of all cyclic subgroups of a finite group $G$, and $\mathcal{O}_{2}(G)$ denotes the number of elements of order $2$ in $G$. In [Marius T., Finite groups with a certain number of cyclic subgroups. The American…