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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Item Type: | Article |
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Item Status: | Live Archive |

## 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. Â© 2003 Plenum Publishing Corporation.

Keywords: | Algebra, Logic |
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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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