|
|
| Line 1: |
Line 1: |
| In [[mathematics]], the '''Alperin–Brauer–Gorenstein theorem''' characterizes the finite [[simple group]]s with [[quasidihedral]] or wreathed<ref>A 2-group is '''wreathed''' if it is a nonabelian [[semidirect product]] of a [[maximal subgroup]] that is a [[direct product of groups|direct product]] of two [[cyclic group]]s of the same order, that is, if it is the [[wreath product]] of a cyclic 2-group with the [[symmetric group]] on 2 points.</ref> [[Sylow subgroup|Sylow 2-subgroups]]. These are isomorphic either to three-dimensional [[projective special linear group]]s or [[projective special unitary group]]s over a [[finite field]]s of odd order, depending on a certain congruence, or to the [[Mathieu group]] <math>M_{11}</math>. {{harvtxt|Alperin|Brauer|Gorenstein|1970}} proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in {{harvtxt|Gorenstein|1968|loc=Ch. 7}}, and presented in some detail in {{harvtxt|Kwon|Lee|Cho|Park|1980}}.
| | Hi there, I am Sophia. Alaska is exactly where he's always been living. What me and my family members adore is performing ballet but I've been using on new issues lately. Office supervising is exactly where her primary earnings arrives from.<br><br>my web-site - spirit messages - [http://modenpeople.co.kr/modn/qna/292291 please click for source] - |
| | |
| ==Notes==
| |
| <references/> | |
| | |
| ==References==
| |
| *{{Citation | last1=Alperin | first1=J. L. | author1-link=J. L. Alperin | last2=Brauer | first2=R. | author2-link=Richard Brauer | last3=Gorenstein | first3=D. | author3-link=Daniel Gorenstein | title=Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups. | doi=10.2307/1995627 | mr=0284499 | year=1970 | journal=[[Transactions of the American Mathematical Society]] | publisher=[[American Mathematical Society]] | issn=0002-9947 | volume=151 | pages=1–261 | jstor=1995627 | issue=1}}
| |
| *{{Citation | last1=Gorenstein | first1=D. | author1-link=Daniel Gorenstein | title=Finite groups | publisher=[[Harper & Row Publishers]] | mr=0231903 | year=1968}}
| |
| *{{Citation | last1=Kwon | first1=T. | last2=Lee | first2=K. | last3=Cho | first3=I. | last4=Park | first4=S. | title=On finite groups with quasidihedral Sylow 2-groups | url=http://kms.or.kr/home/journal/include/downloadPdfJournal.asp?articleuid=%7B71EE4232%2D6997%2D4030%2D8CA7%2D85CDBCB5A2CC%7D | mr=593804 | year=1980 | journal=Journal of the Korean Mathematical Society | issn=0304-9914 | volume=17 | issue=1 | pages=91–97}}
| |
| | |
| {{DEFAULTSORT:Alperin-Brauer-Gorenstein theorem}}
| |
| [[Category:Finite groups]]
| |
| [[Category:Theorems in algebra]]
| |
| | |
| | |
| {{Abstract-algebra-stub}}
| |
Latest revision as of 01:36, 15 November 2014
Hi there, I am Sophia. Alaska is exactly where he's always been living. What me and my family members adore is performing ballet but I've been using on new issues lately. Office supervising is exactly where her primary earnings arrives from.
my web-site - spirit messages - please click for source -