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On Dehn functions of free products of groups
Author(s):
V.
S.
Guba;
M.
V.
Sapir
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1885-1891.
MSC (1991):
Primary 20F32;
Secondary 57M07
Posted:
March 1, 1999
MathSciNet review:
1469408
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Abstract:
In this article we show that the Dehn function of a nontrivial free product of groups is equivalent to its subnegative closure.
References:
- 1.
- G. Baumslag, C. F. Miller III, and H. Short. Isoperimetric inequalities and the homology of groups. Invent. Math., 113:531-560, 1993. MR 95b:57004
- 2.
- M.V. Sapir, J.-C. Birget, E.Rips. Dehn functions of groups, to appear.
- 3.
- S. G. Brick, Dehn functions and products of groups. Trans. Amer. Math. Soc., 335 (1993),369-384. MR 93c:57003
- 4.
- S. Gersten. Isoperimetric and isodiametric functions of finite presentations. In Geometric group theory, Vol. 1 (Sussex, 1991), London Math. Soc. Lecture Note Ser., 181 (1993), 79-96. MR 94f:20066
- 5.
- M. Gromov. Hyperbolic groups. In Essays in Group Theory (S. Gersten, ed.), MSRI Publ. 8. Springer-Verlag, 1987, 75-263. MR 89e:20070
- 6.
- R. C. Lyndon and P. E. Schupp. Combinatorial group theory. Springer-Verlag, 1977. MR 58:28182
- 7.
- K. Madlener, F. Otto. Pseudo-natural algorithms for the word problem for finitely presented monoids and groups. J. Symbolic Computation, 1:383-418, 1985. MR 87h:03067
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Additional Information:
V.
S.
Guba
Affiliation:
Department of Mathematics Vologda State Pedagogical University S. Orlov St.,~6 Vologda~160600 Russia
Email:
guba@vgpi.vologda.su
M.
V.
Sapir
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email:
msapir@math.vanderbilt.edu
DOI:
10.1090/S0002-9939-99-04579-7
PII:
S 0002-9939(99)04579-7
Received by editor(s):
June 27, 1997
Posted:
March 1, 1999
Additional Notes:
The research of the first author was supported in part by grants from the ISF and the Russian Foundation for Fundamental Researches, grant no.~96--01--00420. The research of the second author was supported in part by NSF grants.
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1999,
American Mathematical Society
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