Related papers: Normal restriction in finite groups

We investigate the structure of finite groups whose non-central real class sizes have the same $2$-part. In particular, we prove that such groups are solvable and have $2$-length one. As a consequence, we show that a finite group is…

In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…

Two finite groups $L_1$ and $L_2$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_1$ and $N_2$ such that $L_1\cong G/N_1$ and $L_2\cong G/N_2$. We prove a new sufficient condition for two groups to be…

We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for…

Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…

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}.

There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.

Let $G$ be a finite group, $p$ a prime and $P$ a Sylow $p$-subgroup of $G$. In this note we give a cohomological criterion for the $p$-solvability of $G$ depending on the cohomology in degree $1$ with coefficients in $\mathbb F_p$ of both…

We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential…

This note was prepared as a handout for the MAT401 course ``Polynomial equations and fields", taught at the University of Toronto in Spring 2026. It presents a proof of a necessary condition for the solvability of algebraic equations by…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

In this paper, we establish the theory of $\sigma$-solvable hypergroups, study some properties of $\sigma$-solvable hypergroups and give similar results of Hall's Theorem in $\sigma$-solvable hypergroups.

In this paper, we focus on a question of M. Newman on isomorphic subgroups of solvable groups. We get a reduction theorem of this question: for each prime q, assume that this question holds for every characteristic q-groups, then this…

We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…

Let $\mathbb{E}$ be the HNN-extension of a group $B$ with subgroups $H$ and $K$ associated according to an isomorphism $\varphi\colon H \to K$. Suppose that $H$ and $K$ are normal in $B$ and $(H \cap K)\varphi = H \cap K$. Under these…

We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.

We formulate a set of simple sufficient conditions for the existence of Q-balls in gauge theories.

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

In this paper, we give a necessary and sufficient condition for the finiteness of Galois cohomology of unipotent groups over local fields of positive characteristic

We prove that a uniquely 2-divisible group that admits an almost regular involutory automorphism is solvable.