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Test Elements: From Pro-p to Discrete Groups

Published online by Cambridge University Press:  15 April 2019

By
Ilir Snopce  and
Slobodan Tanushevski
Edited by
C. M. Campbell ,
C. W. Parker ,
M. R. Quick ,
E. F. Robertson  and
C. M. Roney-Dougal
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
C. W. Parker
Affiliation:
University of Birmingham
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
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Summary

We survey some recent results on test elements of pro-p groups and discrete groups. An element g of a group G is a test element of G if every endomorphism of G that fixes g is an automorphism. Our main focus is on pro-p techniques in the study of test elements of discrete groups. In particular, we discuss the distribution of test elements in free groups and surface groups.

Type
Chapter
Information
Groups St Andrews 2017 in Birmingham , pp. 486 - 501
Publisher: Cambridge University Press
Print publication year: 2019

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