Large groups and their periodic quotients

Authors:
A. Yu. Olshanskii and D. V. Osin

Journal:
Proc. Amer. Math. Soc. **136** (2008), 753-759

MSC (2000):
Primary 20F50, 20F05, 20E26

Published electronically:
November 26, 2007

MathSciNet review:
2361846

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Abstract | References | Similar Articles | Additional Information

Abstract: We first give a short group theoretic proof of the following result of Lackenby. If is a large group, is a finite index subgroup of admitting an epimorphism onto a non-cyclic free group, and are elements of , then the quotient of by the normal subgroup generated by is large for all but finitely many . In the second part of this note we use similar methods to show that for every infinite sequence of primes , there exists an infinite finitely generated periodic group with descending normal series , such that and is either trivial or abelian of exponent .

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Additional Information

**A. Yu. Olshanskii**

Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240; and Department of Mathematics, Moscow State University, Moscow, 119899, Russia

Email:
alexander.olshanskiy@vanderbilt.edu

**D. V. Osin**

Affiliation:
Department of Mathematics, The City College of New York, New York, New York 10031

Email:
denis.osin@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-07-09150-2

Received by editor(s):
April 19, 2006

Published electronically:
November 26, 2007

Additional Notes:
The first author was supported in part by the NSF grants DMS 0245600 and DMS 0455881.

The second author was supported in part by NSF grant DMS 0605093. Both authors were supported in part by the Russian Fund for Basic Research grant 05-01-00895.

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.