2019
Том 71
№ 1

All Issues

Endimioni G.

Articles: 1
Article (English)

Hopficity and Co-Hopficity in Soluble Groups

Endimioni G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1335-1341

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.