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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1335 – 1341, October, 2004.
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Endimioni, G. Hopficity and Co-Hopficity in Soluble Groups. Ukr Math J 56, 1594–1601 (2004). https://doi.org/10.1007/s11253-005-0136-4
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DOI: https://doi.org/10.1007/s11253-005-0136-4