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Enrico Jabara

Publications and source records attributed to Enrico Jabara.

7 recordsLinked to original sources
arXiv2021

Extensions of several coprime results to good action case

Let $G$ and $A$ be groups where $A$ acts on $G$ by automorphisms. We say "\textit{the action of $A$ on $G$ is good}" if the equality $% H=[H,B]C_H(B)$ holds for any subgroup $B$ of $A$ and for any $B$-invariant subgroup $H$ of $G$. It is straightforward that every coprime action is a good action. In the present work we extend some results due to Ward, Gross, Shumyatsky, Jabara, and Meng and Guo under coprime action to good action.

math.GR↗
arXiv2020

Recognizing $A_7$ by its set of element orders

Let $G$ be a periodic group, the spectrum $ω(G) \subseteq \mathbb{N}$ of $G$ is the set of orders of elements in $G$. In this paper we prove that the alternating group $A_{7}$ is uniquely defined by its spectrum in the class of all groups.

math.GR↗
arXiv2020

Good action on a finite group

Let $G$ and $A$ be finite groups with $A$ acting on $G$ by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of $A$ on $G$ is good, if $H=[H,B]C_H(B)$ for every subgroup $B$ of $A$ and every $B$-invariant subgroup $H$ of $G.$ This definition allows us to prove a new noncoprime Hall-Higman type theorem. If $A$ is a nilpotent group acting on the finite solvable group $G$ with $C_G(A)=1$, a long standing conjecture states that $h(G)\leq \ell(A)$ where $h(G)$ is the Fitting height of $G$ and $\ell(A)$ is the number of primes dividing the order of $A$ counted with multiplicities. As an application of our result we prove the main theorem of this paper which states that the above conjecture is true if $A$ and $G$ have odd order, the action of $A$ on $G$ is good and some other fairly general conditions are satisfied.

math.GR↗
arXiv2015

A remark on {2,3}-groups with no elements of order six

We describe $\{2,3\}$-groups in which the order of a product of any two elements of orders at most $4$ does not exceed $9$ and the centralizer of every involution is a locally cyclic $2$-subgroup. In particular, we will prove that these groups are locally finite.

math.GR↗
arXiv2015

On the Fitting length of finite soluble groups I

Let $G$ be a finite soluble group and $h(G)$ its Fitting length. The aim of this paper is to give certain upper bounds for $h(G)$ as functions of the Fitting length of at least three Hall subgroups of $G$ which factorize $G$ in a particular way.

math.GR↗
arXiv2013

On the Fitting height of soluble groups admitting a coprime factorisation

In this paper we are concerned with finite soluble groups $G$ admitting a factorisation $G=AB$, with $A$ and $B$ proper subgroups having coprime order. We are interested in bounding the Fitting height of $G$ in terms of some group-invariants of $A$ and $B$: including the Fitting heights and the derived lengths.

math.GR↗