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AUTOCOMMUTATORS AND AUTO-BELL GROUPS
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 Title & Authors
AUTOCOMMUTATORS AND AUTO-BELL GROUPS
Moghaddam, Mohammad Reza R.; Safa, Hesam; Mousavi, Azam K.;
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 Abstract
Let x be an element of a group G and be an automorphism of G. Then for a positive integer n, the autocommutator is defined inductively by and . We call the group G to be n-auto-Engel if for all and every , where . Also, for any integer , 1, a group G is called an n-auto-Bell group when for every and each . In this paper, we investigate the properties of such groups and show that if G is an n-auto-Bell group, then the factor group has finite exponent dividing 2n(n-1), where is the third term of the upper autocentral series of G. Also, we give some examples and results about n-auto-Bell abelian groups.
 Keywords
n-auto-Bell group;autocentral series;autocommutator subgroup;n-auto-Engel group;n-Bell group;
 Language
English
 Cited by
1.
Perfect groups and normal subgroups related to an automorphism, Ricerche di Matematica, 2016  crossref(new windwow)
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