A condition equivalent to the solvability of the endomorphism problem for free groups

Edmunds, Charles C.

doi:10.1090/S0002-9939-1979-0534382-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A condition equivalent to the solvability of the endomorphism problem for free groups
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by Charles C. Edmunds PDF

Proc. Amer. Math. Soc. 76 (1979), 23-24 Request permission

Abstract:

To solve the endomorphism problem for a word W involving n generators of a free group F, it suffices to solve the problem assuming that the images of W involve no more than n generators.

References

Charles C. Edmunds, On the endomorphism problem for free groups. II, Proc. London Math. Soc. (3) 38 (1979), no. 1, 153–168. MR 520977, DOI 10.1112/plms/s3-38.1.153
Paul E. Schupp, On the substitution problem for free groups, Proc. Amer. Math. Soc. 23 (1969), 421–423. MR 245657, DOI 10.1090/S0002-9939-1969-0245657-6

On certain sets of elements in a free group