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Chains of idempotents in endomorphism monoids
B. A. F. Wehrfritz

 

Abstract

If G is a group with finite Hirsch number and with its maximal locally finite normal subgroup satisfying the minimal condition on subgroups, e.g. if G is a finite extension of a torsion-free soluble group of finite rank, then there exists an integer k=k(G) such that for every subgroup H of G any chain of idempotents in the endomorphism monoid End(H) of H has length at most k.

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