{{dablink|"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''' <math>J(P)</math> of a finite ''p''-group ''P'' refers to one of several characteristic subgroups of ''P''. {{harvs|txt|last=Thompson|first=John G.|authorlink=John G. Thompson|year=1964}} originally defined <math>J(P)</math> to be the subgroup generated by the abelian subgroups of ''P'' of maximal rank. More often the Thompson subgroup <math>J(P)</math> 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 <math>J(P)</math>.
==See also==
*Glauberman normal p-complement theorem *ZJ theorem *Puig subgroup, a subgroup analogous to the Thompson subgroup
==References==
*{{Citation | last1=Gorenstein | first1=Daniel | author1-link=Daniel Gorenstein | last2=Lyons | first2=Richard |author2-link=Richard Lyons (mathematician)| last3=Solomon | first3=Ronald |author3-link=Ronald Solomon| title=The classification of the finite simple groups. Number 2. Part I. Chapter G | url=http://www.ams.org/online_bks/surv402 | publisher=American Mathematical Society | location=Providence, R.I. | series=Mathematical Surveys and Monographs | isbn=978-0-8218-0390-5 | mr=1358135 | year=1996 | volume=40}} *{{Citation | last1=Thompson | first1=John G. | author1-link=John G. Thompson | title=Normal p-complements for finite groups | doi=10.1016/0021-8693(64)90006-7 |mr=0167521 | year=1964 | journal=Journal of Algebra | issn=0021-8693 | volume=1 | pages=43–46| doi-access=free }} *{{Citation | last1=Thompson | first1=John G. | author1-link=John G. Thompson | title=A replacement theorem for p-groups and a conjecture | doi=10.1016/0021-8693(69)90068-4 | mr=0245683 | year=1969 | journal=Journal of Algebra | issn=0021-8693 | volume=13 | pages=149–151| doi-access=free }}
Category:Finite groups