Groups with largely splitting automorphisms of orders three and four

Makarenko, N. Yu. and Khukhro, Evgeny (2003) Groups with largely splitting automorphisms of orders three and four. Algebra and Logic, 42 (3). pp. 165-176. ISSN 0002-5232

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Abstract

A subset X of a group G is said to be large (on the left) if, for any finite set of elements g1, . . . , gk â�� G, an intersection of the subsets giX = gix | x â�� X is not empty, that is, â�©i=1k giX â� â� . It is proved that a group in which elements of order 3 form a large subset is in fact of exponent 3. This result follows from the more general theorem on groups with a largely splitting automorphism of order 3, thus answering a question posed by Jaber amd Wagner in 1. For groups with a largely splitting automorphism Ï� of order 4, it is shown that if H is a normal Ï�-invariant soluble subgroup of derived length d then the derived subgroup H,H is nilpotent of class bounded in terms of d. The special case where Ï� = 1 yields the same result for groups that are largely of exponent 4. © 2003 Plenum Publishing Corporation.

Keywords:Algebra, Logic
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15660
Deposited On:11 Nov 2014 18:22

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