Thompson subgroup

{{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 $J(P)$ 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 $J(P)$ 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 $J(P)$ .

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

Thompson subgroup

See also

References