Images of commutator MAPS
作者:
Robert W. Baddeley,
期刊:
Communications in Algebra
(Taylor Available online 1994)
卷期:
Volume 22,
issue 8
页码: 3023-3035
ISSN:0092-7872
年代: 1994
DOI:10.1080/00927879408825010
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
The commutator map θα: G → G associated with the element α of the group G is defined by θα(g) = g−1α−1gα for all g ε G. In this paper we prove that if the image θαis a subgroup of the finite group G, then θα(G) is soluble. (This in fact generalises the well-known result which states that all finite groups that admit a fixed-point-free automorphism are soluble.) An application (that motivated this paper) to the theory of permutation groups is also given.
点击下载:
PDF (368KB)
返 回