Thompson subgroup

Template:Dablink In finite group theory, a branch of mathematics, the Thompson subgroup $J(P)$ of a finite p-group P refers to one of several characteristic subgroups of P. Template:Harvs originally defined $J(P)$ to be the subgroup generated by the abelian subgroups of P of maximal rank. More often the Thompson subgroup $J(P)$ 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 $J(P)$.

See also

• Glauberman normal p-complement theorem
• ZJ theorem
• Puig subgroup, a subgroup analogous to the Thompson subgroup

References

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