Book Review
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Book Information:
Authors:
Alexander Lubotzky and
Dan Segal
Title:
Subgroup growth
Additional book information:
Birkhäuser,
Basel,
2003,
476 pp.,
ISBN 3-7643-6989-2,
$148.00$
[Bas72] Hyman Bass.
The degree of polynomial growth of finitely generated nilpotent groups.
Proc. London Math. Soc. (3), 25:603-614, 1972. MR 0379672
[dSG00] Marcus du Sautoy and Fritz Grunewald.
Analytic properties of zeta functions and subgroup growth.
Ann. of Math. (2), 152(3):793-833, 2000. MR 1815702
[dSS00] Marcus du Sautoy and Dan Segal.
Zeta functions of groups.
In New horizons in pro-
groups, volume 184 of Progr. Math., pages 249-286. Birkhäuser Boston, Boston, MA, 2000. MR 1765124
[Gro81] Mikhael Gromov.
Groups of polynomial growth and expanding maps.
Inst. Hautes Études Sci. Publ. Math., (53):53-73, 1981. MR 0623534
[GSS88] F. J. Grunewald, D. Segal, and G. C. Smith.
Subgroups of finite index in nilpotent groups.
Invent. Math., 93(1):185-223, 1988. MR 0943928
[Hal49] Marshall Hall, Jr.
Subgroups of finite index in free groups.
Canadian J. Math., 1:187-190, 1949. MR 10:506a
[L88] Alexander Lubotzky.
A group theoretic characterization of linear groups.
J. Algebra, 113(1):207-214, 1988. MR 0928062
[LM91] Alexander Lubotzky and Avinoam Mann.
On groups of polynomial subgroup growth.
Invent. Math., 104(3):521-533, 1991. MR 1106747
[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 1239055
[MS90] Avinoam Mann and Dan Segal.
Uniform finiteness conditions in residually finite groups.
Proc. London Math. Soc. (3), 61(3):529-545, 1990. MR 1069514
[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 1433640
[Seg01] Dan Segal.
The finite images of finitely generated groups.
Proc. London Math. Soc. (3), 82(3):597-613, 2001. MR 1816690
[Tit72] Jacques Tits.
Free subgroups in linear groups.
J. Algebra, 20:250-270, 1972. MR 0286898
[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 1044047
[Zel91] Efim I. Zel
manov.
Solution of the restricted Burnside problem for
-groups.
Mat. Sb., 182(4):568-592, 1991. MR 1119009
- [Bas72]
- Hyman Bass.
The degree of polynomial growth of finitely generated nilpotent groups.
Proc. London Math. Soc. (3), 25:603-614, 1972. MR 0379672
- [dSG00]
- Marcus du Sautoy and Fritz Grunewald.
Analytic properties of zeta functions and subgroup growth.
Ann. of Math. (2), 152(3):793-833, 2000. MR 1815702
- [dSS00]
- Marcus du Sautoy and Dan Segal.
Zeta functions of groups.
In New horizons in pro-
groups, volume 184 of Progr. Math., pages 249-286. Birkhäuser Boston, Boston, MA, 2000. MR 1765124
- [Gro81]
- Mikhael Gromov.
Groups of polynomial growth and expanding maps.
Inst. Hautes Études Sci. Publ. Math., (53):53-73, 1981. MR 0623534
- [GSS88]
- F. J. Grunewald, D. Segal, and G. C. Smith.
Subgroups of finite index in nilpotent groups.
Invent. Math., 93(1):185-223, 1988. MR 0943928
- [Hal49]
- Marshall Hall, Jr.
Subgroups of finite index in free groups.
Canadian J. Math., 1:187-190, 1949. MR 10:506a
- [L88]
- Alexander Lubotzky.
A group theoretic characterization of linear groups.
J. Algebra, 113(1):207-214, 1988. MR 0928062
- [LM91]
- Alexander Lubotzky and Avinoam Mann.
On groups of polynomial subgroup growth.
Invent. Math., 104(3):521-533, 1991. MR 1106747
- [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 1239055
- [MS90]
- Avinoam Mann and Dan Segal.
Uniform finiteness conditions in residually finite groups.
Proc. London Math. Soc. (3), 61(3):529-545, 1990. MR 1069514
- [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 1433640
- [Seg01]
- Dan Segal.
The finite images of finitely generated groups.
Proc. London Math. Soc. (3), 82(3):597-613, 2001. MR 1816690
- [Tit72]
- Jacques Tits.
Free subgroups in linear groups.
J. Algebra, 20:250-270, 1972. MR 0286898
- [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 1044047
- [Zel91]
- Efim I. Zel
manov.
Solution of the restricted Burnside problem for
-groups.
Mat. Sb., 182(4):568-592, 1991. MR 1119009
Review Information:
Reviewer:
Rostislav I. Grigorchuk
Affiliation:
Texas A&M University
Email:
grigorch@math.tamu.edu
Journal:
Bull. Amer. Math. Soc.
41 (2004), 253-256
Keywords:
Subgroup growth
Published electronically:
December 16, 2003
Review copyright:
© Copyright 2003
American Mathematical Society