EUDML

In this paper we prove that every $n\in\mathbf{Z}$ can be written as $n=\epsilon_{1}x^{2}_{1}+\epsilon_{2}x^{3}_{2}+\epsilon_{3}x^{4}_{3}+\epsilon_{% 4}x^{5}_{4}$ and as $n=\epsilon_{1}x^{3}_{1}+\epsilon_{2}x^{4}_{2}+\epsilon_{3}x^{5}_{3}+\epsilon_{% 4}x^{6}_{4}+\epsilon_{5}x^{7}_{5}+\epsilon_{6}x^{8}_{6}+\epsilon_{7}x^{9}_{7}+% \epsilon_{8}x^{10}_{8}$ with $x_{i}\in\mathbf{Z}$ and $\epsilon_{i}\in\{-1,1\}$ . We also prove some other results on numbers expressible as sums or differences of unlike powers.

Sugli automorfismi uniformi e privi di coincidenze dei gruppi infiniti

Enrico Jabara — 2007

Bollettino dell'Unione Matematica Italiana

Sia $\Phi$ un gruppo di automorfismi del gruppo $(N,+)$ tale che per ogni $\phi\in\Phi\setminus\{1\}$ la mappa $T_{\phi}\colon N\to N$ $x\mapsto-x+\phi(x)$ sia biiettiva. In questo lavoro si prova che se $N$ è infinito ed è unione di un numero finito di $\Phi$ -orbite, allora $N$ è abeliano.

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

Enrico Jabara — 2005

Czechoslovak Mathematical Journal

In this note we study finite $p$ -groups $G = A B$ 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 $2 n$ .

Every $2$ -group with all subgroups normal-by-finite is locally finite

Enrico Jabara — 2018

Czechoslovak Mathematical Journal

A group $G$ has all of its subgroups normal-by-finite if $H / H_{G}$ is finite for all subgroups $H$ of $G$ . The Tarski-groups provide examples of $p$ -groups ( $p$ a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a $2$ -group with every subgroup normal-by-finite is locally finite. We also prove that if $| H / H_{G} | \leq 2$ for every subgroup $H$ of $G$ , then $G$ contains an Abelian subgroup of index at most $8$ .

Finite groups admitting some coprime operator groups

Enrico Jabara — 2006

Matematički Vesnik

Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito

Egle Bettio; Enrico Jabara — 2011

Bollettino dell'Unione Matematica Italiana

In this paper we prove that a solvable, finitely generated group G of finite torsion-free rank admitting a quasi regular automorphism of prime order is virtually nilpotent. We also prove that the hypothesis that G is finitely generated can be omitted if G is a minimax group.