| 释义 |
- References
In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever g is not in H. The Bender–Suzuki theorem, proved by {{harvtxt|Bender|1971}} extending work of {{harvs|txt|last=Suzuki|year1=1962|year2=1964}}, classifies the groups G with a strongly embedded subgroup H. It states that either - G has cyclic or generalized quaternion Sylow 2-subgroups and H contains the centralizer of an involution
- or G/O(G) has a normal subgroup of odd index isomorphic to one of the simple groups PSL2(q), Sz(q) or PSU3(q) where q≥4 is a power of 2 and H is O(G)NG(S) for some Sylow 2-subgroup S.
{{harvtxt|Peterfalvi|2000|loc=part II}} revised Suzuki's part of the proof.{{harvtxt|Aschbacher|1974}} extended Bender's classification to groups with a proper 2-generated core.References- {{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=Finite groups with a proper 2-generated core | jstor=1996929 | mr=0364427 | year=1974 | journal=Transactions of the American Mathematical Society | issn=0002-9947 | volume=197 | pages=87–112 | doi=10.2307/1996929}}
- {{Citation | last1=Bender | first1=Helmut | title=Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläβt | doi=10.1016/0021-8693(71)90008-1 | mr=0288172 | year=1971 | journal=Journal of Algebra | issn=0021-8693 | volume=17 | pages=527–554}}
- {{Citation | last1=Peterfalvi | first1=Thomas | title=Character theory for the odd order theorem | publisher=Cambridge University Press | series=London Mathematical Society Lecture Note Series | isbn=978-0-521-64660-4 | mr=1747393 | year=2000 | volume=272|url=https://books.google.com/books?isbn=052164660X}}
- {{Citation | last1=Suzuki | first1=Michio | author1-link=Michio Suzuki | title=On a class of doubly transitive groups | jstor=1970423 | mr=0136646 | year=1962 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=75 | pages=105–145 | doi=10.2307/1970423}}
- {{Citation | last1=Suzuki | first1=Michio | author1-link=Michio Suzuki | title=On a class of doubly transitive groups. II | jstor=1970408 | mr=0162840 | year=1964 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=79 | pages=514–589 | doi=10.2307/1970408}}
1 : Finite groups |