Book Review
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MathSciNet review:
2816391
Full text of review:
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Book Information:
Author:
Dan Segal
Title:
Words: notes on verbal width in groups
Additional book information:
London Mathematical Society Lecture Note Series, Vol. 361,
Cambridge University Press,
Cambridge,
2009,
xii+121 pp.,
ISBN 978-0-521-74766-0
W. Burnside. On an unsettled question in the theory of discontinuous groups. Quart. J. Pure Appl. Math., 33:230–238, 1902.
Andrei Jaikin-Zapirain, On the verbal width of finitely generated pro-$p$ groups, Rev. Mat. Iberoam. 24 (2008), no. 2, 617–630. MR 2459206, DOI 10.4171/RMI/549
Michael Larsen and Aner Shalev, Word maps and Waring type problems, J. Amer. Math. Soc. 22 (2009), no. 2, 437–466. MR 2476780, DOI 10.1090/S0894-0347-08-00615-2
Martin W. Liebeck, E. A. O’Brien, Aner Shalev, and Pham Huu Tiep, The Ore conjecture, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 4, 939–1008. MR 2654085, DOI 10.4171/JEMS/220
Ju. I. Merzljakov, Algebraic linear groups as full groups of automorphisms and the closure of their verbal subgroups, Algebra i Logika Sem. 6 (1967), no. 1, 83–94 (Russian, with English summary). MR 0213364
H. Neumann. Varieties of groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1967.
Nikolay Nikolov and Dan Segal, On finitely generated profinite groups. II. Products in quasisimple groups, Ann. of Math. (2) 165 (2007), no. 1, 239–273. MR 2276770, DOI 10.4007/annals.2007.165.239
Dan Segal, Words: notes on verbal width in groups, London Mathematical Society Lecture Note Series, vol. 361, Cambridge University Press, Cambridge, 2009. MR 2547644, DOI 10.1017/CBO9781139107082
Jean-Pierre Serre, Galois cohomology, Springer-Verlag, Berlin, 1997. Translated from the French by Patrick Ion and revised by the author. MR 1466966, DOI 10.1007/978-3-642-59141-9
Aner Shalev, Word maps, conjugacy classes, and a noncommutative Waring-type theorem, Ann. of Math. (2) 170 (2009), no. 3, 1383–1416. MR 2600876, DOI 10.4007/annals.2009.170.1383
References
- W. Burnside. On an unsettled question in the theory of discontinuous groups. Quart. J. Pure Appl. Math., 33:230–238, 1902.
- A. Jaikin-Zapirain. On the verbal width of finitely generated pro-$p$ groups. Revista Mat. Iberoamericana, 24:617–630, 2008. MR 2459206 (2010a:20058)
- Michael Larsen and Aner Shalev. Word maps and Waring type problems. J. Amer. Math. Soc., 22(2):437–466, 2009. MR 2476780 (2010d:20019)
- Martin W. Liebeck, E. A. O’Brien, Aner Shalev, and Pham Huu Tiep. The Ore conjecture. J. Eur. Math. Soc. (JEMS), 12(4):939–1008, 2010. MR 2654085
- Yu. I. Merzlyakov. Algebraic linear groups as full groups of automorphisms and the closure of their verbal subgroups. Algebra i Logika Sem., 6(1):83–94, 1967. (Russian; English summary). MR 0213364 (35:4228)
- H. Neumann. Varieties of groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1967.
- N. Nikolov and D. Segal. On finitely generated profinite groups, I: strong completeness and uniform bounds. Ann. of Math. (2), 165:239–273, 2007. MR 2276770 (2008f:20053)
- D. Segal. Words: notes on verbal width in groups. London Mathematical Society Lecture Note Series., 361, Cambridge University Press, 2009. MR 2547644 (2011a:20055)
- Jean-Pierre Serre. Galois cohomology. Springer-Verlag, Berlin, 1997. MR 1466966 (98g:12007)
- Aner Shalev. Word maps, conjugacy classes, and a noncommutative Waring-type theorem. Ann. of Math. (2), 170(3):1383–1416, 2009. MR 2600876
Review Information:
Reviewer:
V. Nekrashevych
Affiliation:
Texas A&M University, College Station, Texas
Email:
nekrash@math.tamu.edu
Journal:
Bull. Amer. Math. Soc.
48 (2011), 491-494
DOI:
https://doi.org/10.1090/S0273-0979-2011-01333-7
Published electronically:
March 25, 2011
Review copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
