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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-104/6/d/ii/solution

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Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 104 / 6 / d / ii / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-06

Part (c) shows that every finitely presented group embeds in a finitely presented group with no nontrivial finite quotients of a group. Consequently this property also has no possible forbidden witness

A_{-}

. Therefore

Having no nontrivial finite quotients is not a Markov property .

(1)

Both properties have positive witnesses, for example

C_{2}

and the trivial group respectively. It is the required embedding obstruction that fails in each case.

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