2017
Том 69
№ 6

All Issues

Hopficity and Co-Hopficity in Soluble Groups

Endimioni G.

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Abstract

We show that a soluble group satisfying the minimal condition for its normal subgroups is co-hopfian and that a torsion-free finitely generated soluble group of finite rank is hopfian. The latter property is a consequence of a stronger result: in a minimax soluble group, the kernel of an endomorphism is finite if and only if its image is of finite index in the group.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 10, pp 1594-1601.

Citation Example: Endimioni G. Hopficity and Co-Hopficity in Soluble Groups // Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1335-1341.

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