In mathematical
finite group theory
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
, the uniqueness case is one of the three possibilities for groups of
characteristic 2 type given by the
trichotomy theorem.
The uniqueness case covers groups ''G'' of characteristic 2 type with ''e''(''G'') ≥ 3 that have an almost strongly ''p''-embedded maximal 2-local subgroup for all primes ''p'' whose 2-local ''p''-rank is sufficiently large (usually at least 3).
proved that there are no finite simple groups in the uniqueness case.
References
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*{{Citation , last1=Stroth , first1=Gernot , editor1-last=Arasu , editor1-first=K. T. , editor2-last=Dillon , editor2-first=J. F. , editor3-last=Harada , editor3-first=Koichiro , editor4-last=Sehgal , editor4-first=S. , editor5-last=Solomon. , editor5-first=R. , title=Groups, difference sets, and the Monster (Columbus, OH, 1993) , publisher=de Gruyter , location=Berlin , series=Ohio State Univ. Math. Res. Inst. Publ. , isbn=978-3-11-014791-9 , mr=1400413 , year=1996 , volume=4 , chapter=The uniqueness case , pages=117–126
Finite groups