Help


[permalink] [id link]
+
Page "Finite group" ¶ 5
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Every and group
Every finite simple group is isomorphic to one of the following groups:
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
* Every group G acts on G, i. e. in two natural but essentially different ways:, or.
Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every instrumental group ( or section ) has a principal who is generally responsible for leading the group and playing orchestral solos.
* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.
While he admits the existence of caste-based discrimination, he writes that " Every social group cannot be regarded as a race simply because we want to protect it against prejudice and discrimination ".
Every local group is required to have a seneschal who reports to the kingdom's seneschal.
Every local group is required to have one.
* Every topological group is completely regular.
Every summer the group gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying the splendors of the Gilded Age.
* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem
Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.
Every group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
Every subgroup of a topological group is itself a topological group when given the subspace topology.
:" Every group is naturally isomorphic to its opposite group "
Every ten years, when the general census of population takes place, each citizen has to declare which linguistic group they belong or want to be aggregated to.

Every and prime
Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
# Every prime ideal of A is principal.
Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.
Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3.
* Hardy and Littlewood listed as their Conjecture I: " Every large odd number ( n > 5 ) is the sum of a prime and the double of a prime.
Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.
Every strong probable prime to base a is also an Euler probable prime to the same base, but not vice versa.
Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
: Every oriented prime closed 3-manifold can be cut along tori, so that the interior of each of the resulting manifolds has a geometric structure with finite volume.
Every non-zero characteristic is a prime number.
: Every Boolean algebra contains a prime ideal.
* Every number of the form 2 < sup > m </ sup > p for a natural number m and a prime number p such that p < 2 < sup > m + 1 </ sup > is also semiperfect.
Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.
Every imperfect field is necessarily transcendental over its prime subfield ( the minimal subfield ), because the latter is perfect.
A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group of the form for some prime number p and some positive integer n. Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.
* Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.

Every and order
Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.
Every six months the presidency rotates between the states, in an order predefined by the Council's members, allowing each state to preside over the body.
Most of his films have been at least partially financed by Telefilm Canada, and Cronenberg is a vocal supporter of government-backed film projects, saying " Every country needs system of government Grant ( money ) | grants in order to have a national cinema in the face of Hollywood ".
Every subfield of an ordered field is also an ordered field in the inherited order.
* Every totally ordered set with the order topology is Tychonoff.
Every thing depends upon the evil of the second order ; it is this which gives to such actions the character of crime, and which makes punishment necessary.
Every number is thought of as a decimal fraction with the initial decimal point omitted, which determines the filing order.
Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set.
Maxwell Fyfe brought up Raeder's order of 15 October 1939, which read: " Measures which are considered necessary from a military point of view will have to be carried out, even if they are not covered by existing international law ... Every protest from neutral powers will have to be turned down ... The more ruthlessly economic warfare is waged ... the sooner the war will come to an end ".
Every composite number can be written as the product of two or more ( not necessarily distinct ) primes ; furthermore, this representation is unique up to the order of the factors.
; Non-imposition: ( or citizen sovereignty ) Every possible societal preference order should be achievable by some set of individual preference orders.
Every member of the Bene Gesserit is conditioned into singular loyalty to the order and its goals with allegiances to even family being secondary, and no goal is more paramount than the Sisterhood's large-scale breeding program.
Every TIFF begins with a 2-byte indicator of byte order: " II " for little-endian ( aka " intel byte ordering ", circa 1980 ) and " MM " for big-endian ( aka " motorola byte ordering ", circa 1980 ) byte ordering.
Every Edwards curve with a point of order 3 can be written in the ways shown above.
Every year the Hopduvelfeesten is organised after the hop harvest in order to have a good harvest in the following years.
Every school within the Institute does require that applicants send in an artist's statement, along with a portfolio or audition ( depending on the program ) in order to be considered for admission.
Every person born into this world comes from one of these categories in order to help fulfill the kind of function that that category of people is supposed to fulfill in order to keep the community together.
Every cylinder added beyond five increases the overlap of firing strokes and makes for less primary order vibration.
# Every word must be explained in all its meanings, in order that different interpretations may be found.
Every association of men is necessarily a separation from other men ... the political thus understood is not the constitutive principle of the state, of order, but a condition of the state.
* Every glass in my recent order was chipped.
Every start of a semester a renewal is necessary in order to continue parking in Lot # 3A.
Every year at the beginning of June, the female turtles come to the southern beaches in order to bury their eggs in the sand.

0.292 seconds.