Abstract
This article is based on a talk that the author gave at Groups in Galway 2005. We discuss four conjectures, known to be false, and give a progress report on finding min- imal counterexamples for them. These conjectures are varia- tions on the 47 (false) conjectures Desmond MacHale gave in his 1981 paper Minimum Counterexamples in Group The- ory. My variations are on an Irish tune, the theme is in Desmond MacHale's 1981 paper Minimum Counterexamples in Group The- ory (7). In this paper, 47 conjectures are stated, all known to be false, and MacHale asks for minimal counterexamples. Conjecture 7 in (7) reads as follows. Conjecture 7. In any group G, the set of commutators forms a subgroup.
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