|
Uniqueness Case
In mathematical finite group theory Finite is the opposite of infinite. It may refer to: * Finite number (other) * 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 * * *{{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-fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group Theory
Finite is the opposite of infinite. It may refer to: * Finite number (other) * 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 for person and/or tense or aspect * "Finite", a song by Sara Groves from the album ''Invisible Empires'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause * a non-finite clause is a clause whose main verb is non-finite See also * Infinite (other) Infin ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic (algebra)
In mathematics, the characteristic of a ring , often denoted , is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero. That is, is the smallest positive number such that: :\underbrace_ = 0 if such a number exists, and otherwise. Motivation The special definition of the characteristic zero is motivated by the equivalent definitions characterized in the next section, where the characteristic zero is not required to be considered separately. The characteristic may also be taken to be the exponent of the ring's additive group, that is, the smallest positive integer such that: :\underbrace_ = 0 for every element of the ring (again, if exists; otherwise zero). Some authors do not include the multiplicative identity element in their requirements for a ring (see Multiplicative identity and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trichotomy Theorem
In group theory, the trichotomy theorem divides the finite simple groups of characteristic 2 type and rank at least 3 into three classes. It was proved by for rank 3 and by for rank at least 4. The three classes are groups of GF(2) type In mathematical finite group theory, a group of GF(2)-type is a group with an involution centralizer whose generalized Fitting subgroup is a group of symplectic type . As the name suggests, many of the groups of Lie type over the field with 2 el ... (classified by Timmesfeld and others), groups of "standard type" for some odd prime (classified by the Gilman–Griess theorem and work by several others), and groups of uniqueness type, where Aschbacher proved that there are no simple groups. References * * * Theorems about finite groups {{algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |