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### 2-Groups which Contain Exactly Three Involutions.

Mathematische Zeitschrift

### A Cohomological Property of Regular p-Groups.

Mathematische Zeitschrift

### A Frobenius Theorem for Blocks.

Inventiones mathematicae

### A generalized Frattini subgroup of a finite group.

International Journal of Mathematics and Mathematical Sciences

### A new characterization of symmetric group by NSE

Czechoslovak Mathematical Journal

Let $G$ be a group and $\omega \left(G\right)$ be the set of element orders of $G$. Let $k\in \omega \left(G\right)$ and ${m}_{k}\left(G\right)$ be the number of elements of order $k$ in $G$. Let nse$\left(G\right)=\left\{{m}_{k}\left(G\right):k\in \omega \left(G\right)\right\}$. Assume $r$ is a prime number and let $G$ be a group such that nse$\left(G\right)=$ nse$\left({S}_{r}\right)$, where ${S}_{r}$ is the symmetric group of degree $r$. In this paper we prove that $G\cong {S}_{r}$, if $r$ divides the order of $G$ and ${r}^{2}$ does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.

### A note on a class of factorized $p$-groups

Czechoslovak Mathematical Journal

In this note we study finite $p$-groups $G=AB$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$. As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index ${p}^{n-1}$ then $G$ has derived length at most $2n$.

### A note on groups with hamiltonian quotients

Rendiconti del Seminario Matematico della Università di Padova

### A note on hamiltonian 2-groups

Rendiconti del Seminario Matematico della Università di Padova

### A note on loops of square-free order

Commentationes Mathematicae Universitatis Carolinae

Let $Q$ be a loop such that $|Q|$ is square-free and the inner mapping group $I\left(Q\right)$ is nilpotent. We show that $Q$ is centrally nilpotent of class at most two.

### A note on the minimal normal Fitting class

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Un gruppo finito ciclico-per-nilpotente appartiene alla minima classe di Fitting normale se e solo se è nilpotente.

### A remark on operating groups.

International Journal of Mathematics and Mathematical Sciences

### A result about cosets

Rendiconti del Seminario Matematico della Università di Padova

### Abelian quasinormal subgroups of groups

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$. If $n$ is any positive integer, either odd or divisible by $4$, then we prove that the subgroup ${A}^{n}$ is also quasinormal in $G$.

### About noncommuting graphs.

Sibirskij Matematicheskij Zhurnal

### Algebre di Lie graduate in caratteristica due

Bollettino dell'Unione Matematica Italiana

### An algorithm for the word problem in $HNN$ extensions and the dependence of its complexity on the group representation

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

### Analoga des Fundamentalsatzes der projektiven Geometrie in der Gruppentheorie. II

Rendiconti del Seminario Matematico della Università di Padova

### Analoga des Fundamentalsatzes der projektiven Geometrie in der Gruppentheorie - I

Rendiconti del Seminario Matematico della Università di Padova

### Another Homological Characterisation of Finite p-Nilpotent Groups.

Mathematische Zeitschrift

### Automorfismi involutori di p-gruppi finiti

Rendiconti del Seminario Matematico della Università di Padova

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