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Thompson subgroup

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"Thompson subgroup" can also mean an analogue of the Weyl group used in the classical involution theorem

In finite group theory, a branch of mathematics, the Thompson subgroup J ( P ) {\displaystyle J(P)} of a finite p-group P refers to one of several characteristic subgroups of P. John G. Thompson (1964) originally defined J ( P ) {\displaystyle J(P)} to be the subgroup generated by the abelian subgroups of P of maximal rank. More often the Thompson subgroup J ( P ) {\displaystyle J(P)} is defined to be the subgroup generated by the abelian subgroups of P of maximal order or the subgroup generated by the elementary abelian subgroups of P of maximal rank. In general these three subgroups can be different, though they are all called the Thompson subgroup and denoted by J ( P ) {\displaystyle J(P)} .

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