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Test Elements: From Pro-p to Discrete Groups

Published online by Cambridge University Press:  15 April 2019

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.

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Publisher: Cambridge University Press
Print publication year: 2019

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