Giovanni Cutolo: papers

UNINA
13
G. Cutolo and C. Nicotera
A note on endomorphisms of hypercentral groups
J. Algebra, 255, (2002), pp. 164–173.
doi: 10.1016/s0021-8693(02)00118-7
MathSciNet Zentralblatt Comments Abstract Full Text
14
G. Cutolo and C. Nicotera
Subgroups defining automorphisms in locally nilpotent groups
Forum Math., 15, (2003), pp. 489–506.
doi: 10.1515/form.2003.027
MathSciNet Zentralblatt Comments Abstract Full Text

These two papers, jointly written with Chiara Nicotera, are about what we called bases with respect to sets of automorphisms (or endomorphisms). The terminology is reminescent of that used for permutation groups: a basis for a set S of endomorphisms of a group G is a subset X of G such that two elements of S coincide if (and only if) they have the same restrictions to X. In both papers we are mainly concerned with nilpotency conditions. While the motivation of [13] is finding bases (explicitly) in classes of locally nilpotent groups, the main focus in [14] is: what can be said on the structure of a group given some information on (the subgroup generated by) a basis? (any set of generators is always a basis, of course). There are still several special cases of this general question to be answered. There are obvious relation between the cardinality of a group of automorphisms and that of a (corresponding) basis, thus one of the results in [14] proves the existence of outer automorphisms in some countable locally nilpotent groups (the theorem yielding this consequence is stated in slightly incorrect form in the MSN review).

Don't be fooled by the order of publication: [14] comes first: it was written, submitted and accepted before [13] was done.

Besides the references cited in the papers, Arturo Magidin pointed out that other problems of a similar nature had been previously studied in a series of papers by John Isbell; the latest one is on Semigroup Forum, vol. 7 (1974) p.364–368).

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