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Book Review

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Book Information

Author(s): Alexander Lubotzky and Dan Segal
Title: Subgroup growth
Additional book information: Birkhäuser, Basel, 2003, 476, $148.00, 3-7643-6989-2

References:

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Hyman Bass.
The degree of polynomial growth of finitely generated nilpotent groups.
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[dSG00]
Marcus du Sautoy and Fritz Grunewald.
Analytic properties of zeta functions and subgroup growth.
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[dSS00]
Marcus du Sautoy and Dan Segal.
Zeta functions of groups.
In New horizons in pro-$p$ groups, volume 184 of Progr. Math., pages 249-286. Birkhäuser Boston, Boston, MA, 2000. MR 2001h:11123

[Gro81]
Mikhael Gromov.
Groups of polynomial growth and expanding maps.
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[GSS88]
F. J. Grunewald, D. Segal, and G. C. Smith.
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[Hal49]
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Subgroups of finite index in free groups.
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[L88]
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J. Algebra, 113(1):207-214, 1988. MR 89c:20066

[LM91]
Alexander Lubotzky and Avinoam Mann.
On groups of polynomial subgroup growth.
Invent. Math., 104(3):521-533, 1991. MR 92d:20038

[LMS93]
Alexander Lubotzky, Avinoam Mann, and Dan Segal.
Finitely generated groups of polynomial subgroup growth.
Israel J. Math., 82(1-3):363-371, 1993. MR 95b:20051

[MS90]
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Proc. London Math. Soc. (3), 61(3):529-545, 1990. MR 91j:20093

[P]
Laszlo Pyber.
Groups of intermediate subgroup growth and a problem of Grothendieck.
To appear.

[PS96]
Laszlo Pyber and Aner Shalev.
Groups with super-exponential subgroup growth.
Combinatorica, 16(4):527-533, 1996. MR 98g:20044

[Seg01]
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Proc. London Math. Soc. (3), 82(3):597-613, 2001. MR 2002b:20033

[Tit72]
Jacques Tits.
Free subgroups in linear groups.
J. Algebra, 20:250-270, 1972. MR 44:4105

[Zel90]
Efim I. Zel$'$manov.
Solution of the restricted Burnside problem for groups of odd exponent.
Izv. Akad. Nauk SSSR Ser. Mat., 54(1):42-59, 221, 1990. MR 91i:20037

[Zel91]
Efim I. Zel$'$manov.
Solution of the restricted Burnside problem for $2$-groups.
Mat. Sb., 182(4):568-592, 1991. MR 93a:20063

Additional Information:

Reviewer(s):
Rostislav I. Grigorchuk
Affiliation: Texas A&M University
Email: grigorch@math.tamu.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 41 (2004), 253-256.

MSC (2000): Primary 20E07
DOI: 10.1090/S0273-0979-03-01003-6
PII: S 0273-0979(03)01003-6
Keywords: Subgroup growth
Posted: December 16, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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