Thompson factorization: Difference between revisions

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{{Short description|Mathematical theory}}

{{Underlinked|date=November 2012}}

In mathematical[[Group theory#Finite group theory|finite group theory]], a branch of [[mathematics]], a '''Thompson factorization''', introduced by {{harvs|txt|authorlink=John G. Thompson|year=1966|last=Thompson}}, is an expression of some [[finite groupsgroup]]s as a product of two subgroups[[subgroup]]s, usually [[centralizer and normalizer|normalizers]] or [[centralizer and normalizer|centralizers]] of [[p-group|''p''-subgroups]] for some [[prime number|prime]] ''p''.

In mathematical finite group theory, a '''Thompson factorization''', introduced by {{harvs|txt|authorlink=John G. Thompson|year=1966|last=Thompson}}, is an expression of some finite groups as a product of two subgroups, usually normalizers or centralizers of ''p''-subgroups for some prime ''p''.

==References==

*{{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=Finite group theory | publisher=[[Cambridge University Press]] | edition=2nd | series=Cambridge Studies in Advanced Mathematics | isbn= 0-521-78145-0 | mr=1777008 | year=2000 | volume=10}}

*{{Citation | last1=Aschbacher | first1=Michael | author1-linktitle=MichaelOn Aschbacherthe |failure title=Finiteof groupthe theoryThompson factorization in 2-constrained groups | publisherdoi=[[Cambridge10.1112/plms/s3-43.3.425 University| Press]]mr=635564 | editionyear=2nd1981 | seriesjournal=CambridgeProceedings Studiesof inthe AdvancedLondon MathematicsMathematical Society |series=Third isbnSeries | issn=978-0-5210024-78145-9; 978-0-521-78675-16115 | mrvolume=177700843 | yearissue=20003 | volumepages=10425–449}}

*{{Citation | last1=AschbacherThompson | first1=MichaelJohn G. | author1-link=MichaelJohn AschbacherG. Thompson | title=On the failureFactorizations of the Thompson factorization in 2''p''-constrainedsolvable groups | doiurl=10.1112http:/plms/s3-43projecteuclid.3org/euclid.425pjm/1102994982 | mr=6355640188296 | year=19811966 | journal=Proceedings[[Pacific Journal of the London Mathematical Society. Third SeriesMathematics]] | issn=00240030-61158730 | volume=4316 | issue=32 | pages=425–449371–372 | doi=10.2140/pjm.1966.16.371| doi-access=free }}

*{{Citation | last1=Thompson | first1=John G. | author1-link=John G. Thompson | title=Factorizations of ''p''-solvable groups | url=http://projecteuclid.org/euclid.pjm/1102994982 | mr=0188296 | year=1966 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=16 | pages=371–372}}

[[Category:Finite groups]]

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