This article is cited in 7 papers

The Congruence Property of AT-Groups

E. L. Pervova


Abstract: An AT-group is said to possess the congruence property if every normal subgroup of that group contains a congruence subgroup. We construct a series of examples of periodic AT-groups without this property. Moreover, we give an example of a periodic group which has a decidable conjugacy problem but lacks conjugacy separability.

Keywords: AT-group, periodic group, congruence property, conjugacy problem, conjugacy separability.

UDC: 512.544.4

Received: 28.07.2000

 English version: Algebra and Logic, 2002, 41:5, 306–313

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