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A Note on the Hopficity of Finitely Generated Free-by-Nilpotent Groups

Published online by Cambridge University Press:  20 November 2018

James Boler
James Boler*
Affiliation:
Oklahoma State University Stillwater, Oklahoma
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Our purpose is to deduce from a theorem of P. Hall the following observation.

Let G be a finitely generated group and F a free normal subgroup of G with G/F nilpotent. Then G is hopfian.

Here a group G is hopfian if every epiendomorphism G→G is an automorphism.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 33 - 34
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Baumslag, G., Finitely generated cyclic extensions of free groups are residually finite, Bull. Aus. Math. Soc. 5 (1971), 87-94.Google Scholar
2. Baumslag, G. and Solitar, D., Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199-201.Google Scholar
3. Bieri, R., Normal subgroups in duality groups and in groups of cohomological dimension 2, Jour. Pure Appl. Alg. 7 (1976), 35-51.Google Scholar
4. Hall, P., On the finiteness of certain soluble groups, Proc. Lond. Math. Soc. (3) 9 (1959), 595-622.Google Scholar
5. Mal'cev, A. I., On isomorphic matrix representations of infinite groups, Mat. Sbornik 8 (1940), 405-422.Google Scholar
6. Newman, B. B., Some results on one-relator groups, Bull. Amer. Math. Soc. 74 (1968), 568-571.Google Scholar