High Quality Content by WIKIPEDIA articles! In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted F, T and V, which were first studied by the logician Richard Thompson in 1965. Of the three, F is the most widely studied, and is sometimes referred to as the Thompson group or Thompson's group. The Thompson groups, and F in particular, have a collection of unusual properties which have made them counterexamples to many general conjectures in group theory. All three Thompson groups are infinite but finitely presented. T and V are (rare) examples of infinite but finitely-presented simple groups. The group F is "just non-abelian" in the sense that it is not abelian, but all its proper homomorphic images are abelian.

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