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In mathematics, the term Thompson group or Thompson's group can refer to either

• The finite Thompson sporadic group Th studied by John G. Thompson
• The finite Thompson subgroup of a p-group, the subgroup generated by the abelian subgroups of maximal order.
• "Thompson subgroup" can also mean an analogue of the Weyl group used in the classical involution theorem
• The infinite Thompson groups F, T and V studied by the logician Richard Thompson.

Outside of mathematics, it may also refer to

• Thompson Group Inc.