UID:
almafu_9959227369002883
Format:
1 online resource (xi, 121 pages) :
,
digital, PDF file(s).
ISBN:
1-107-19340-0
,
1-139-10708-9
,
1-283-29579-2
,
9786613295798
,
1-139-12249-5
,
1-139-11675-4
,
1-139-12741-1
,
1-139-11239-2
,
1-139-11458-1
Series Statement:
London Mathematical Society lecture note series ; 361
Content:
After a forty-year lull, the study of word-values in groups has sprung back into life with some spectacular new results in finite group theory. These are largely motivated by applications to profinite groups, including the solution of an old problem of Serre. This book presents a comprehensive account of the known results, both old and new. The more elementary methods are developed from scratch, leading to self-contained proofs and improvements of some classic results about infinite soluble groups. This is followed by a detailed introduction to more advanced topics in finite group theory, and a full account of the applications to profinite groups. The author presents proofs of some very recent results and discusses open questions for further research. This self-contained account is accessible to research students, but will interest all research workers in group theory.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover; Title; Copyright; Contents; Preface; 1 Generalities; 1.1 Basic concepts; 1.2 Commutators; 1.3 Generalized words; 1.4 Conciseness; 2 Verbally elliptic classes; 2.1 Virtually nilpotent groups; 2.2 Group ring stuff; 2.3 Results of Peter Stroud and Keith George; 2.4 Extracting roots in nilpotent groups; 2.5 Virtually-nilpotent supplements; 2.6 Virtually minimax groups; 3 Words of infinite width; 3.1 Free groups; 3.2 Commutators in p-groups; 4 Words and profinite groups; 4.1 Verbal subgroups in profinite groups; 4.2 Open subgroups; 4.3 Pronilpotent groups; 4.4 Variety stuff
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4.5 Words of infinite width in pro-p groups4.6 Finite simple groups; 4.7 The Nikolov-Segal theorems; 4.8 Uniformly elliptic words; 4.9 On J-varieties; 5 Algebraic and analytic groups; 5.1 Algebraic groups; 5.2 Adelic groups; 5.3 On just-infinite profinite groups; 5.4 p-adic analytic groups; 5.5 Analytic stuff; Appendix: the problems; Bibliography; Index
,
English
Additional Edition:
ISBN 0-521-74766-X
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9781139107082
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