Enrico Jabara

Finite groups whose noncentral commuting elements have centralizers of equal size.

(y). An important subclass of F-groups is the class of I-groups, in which all centralizers of noncentralelements are of the same order. Ito proved in [I] that I-groups arenilpotent and they are direct products of an abelian group and a groupof prime-power order. Only 49 years later, K. Ishikawa showed in [Ish]that groups in I are of class at most 3. For a simpler proof, see thepapers of A. Mann [M1] and of M. Isaacs [Is]. The F-groups wereinvestigated by J. Rebmann in [R]. He determined their strucure, upto that of F-groups which are central extensions of groups of prime-power order.Another important subclass of F-groups is the class of CA-groups,consisting of groups in which all centralizers of noncentral elementsare abelian. The CA-groups (or rather the equivalent class of M-groups) were investigated by R. Schmidt in [S] (see also [S1], Theorem9.3.12). He determined their structure up to that of CA-groups whichare central extensions of groups of prime-power order. It is very similarto the structure of F-groups.

Fixed point free actions of groups of exponent 5

In this paper we prove that if V is a vector space over a field of positive characteristic p 6D 5 then any regular subgroup A of exponent 5 of GL .V/ is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

On the Fitting height of factorised soluble groups

Abstract In this paper we are concerned with finite soluble groups G admitting a factorisation G=AB

Some groups of exponent 72

{G=AB}

On groups of exponent 36

, 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.

Gruppi che ammettono un automorfismo 4-spezzante

Abstract Local finiteness is proved for groups of exponent dividing 72 with no elements of order 6.

Finite group with Hall coverings

Locally finiteness is proved for a group of exponent 36 containing an involution and no elements of order 6.

On {2, 3}-groups without elements of order 6

AbstractLetG be a group admitting a 4-splitting automorphism (i.e. an automorphism σ such that

On sharply 2-transitive groups with point stabilizer of exponent 2n⋅3

gg^\sigma g^{\sigma ^2 } g^{\sigma ^3 } = 1