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* Every finitely-generated locally cyclic group is cyclic.
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Every and finitely-generated
* Every finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian.
Every finitely-generated R-module is a direct sum of these.
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 and locally
* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.
Every regular space is locally regular, but the converse is not true.
*( BCT2 ) Every locally compact Hausdorff space is a Baire space.
* Roslyn Sunday Market – Every Sunday from June through September, this outdoor farmer's market and craft fair is located on Pennsylvania Avenue in downtown Roslyn and offers a selection of local fruits, vegetables, arts, crafts and locally produced specialty items.
*( BCT2 ) Every locally compact Hausdorff space is a Baire space.
Every constant function is locally constant.
Every locally constant function from the real numbers R to R is constant by the connectedness of R. But the function f from the rationals Q to R, defined by f ( x ) = 0 for x < π, and f ( x ) = 1 for x > π, is locally constant ( here we use the fact that π is irrational and that therefore the two sets
* Every cyclic group is locally cyclic, and every locally cyclic group is abelian.
* Every subgroup and quotient group of a locally cyclic group is locally cyclic.
: Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.
* Every locally compact space is compactly generated.
Every year ; on the Sunday after Easter, the village holds a Brawn eating competition ( known locally as Pork Cheese ).
Every year Exhibition ( Mela ) locally called as ' Urus ' takes place.
Every October is " Apple Day " when the apples are harvested from locally owned orchards.
Every Friday of the year is locally known as Quiapo Day, and is dedicated to the Black Nazarene, with the novena being held not only in the basilica but in other churches nationwide.
Every Monday, Wednesday and Saturday a lively open air market was held featuring fresh locally raised produce, poultry and locally crafted artefacts.
Every closed subgroup of a locally compact group is locally compact.
Every and cyclic
Every simple module is cyclic, that is it is generated by one element.
Every group of prime order is cyclic, since Lagrange's theorem implies that the cyclic subgroup generated by
Note: Every cyclic permutation of definition type 1 will be constructed
Note: Every permutation over a set with k elements is a cyclic permutation of definition type 2 if and only if it is a cyclic permutation of definition type 1 with gcd ( k, offset )
Note: Every cyclic permutation of definition type 3 may be seen as an union of a cyclic permutation of definition type 2 and some fixed points.
Every cyclic permutation of definition type 2 may be seen ″ as a cyclic permutation of definition type 3 with zero fixed points.
Every prime power ( except powers of 2 ) has a primitive root ; thus the multiplicative group of integers modulo p < sup > n </ sup > ( or equivalently, the unit group of the ring ) is cyclic.
* Every cyclic shift and the inverse of a cyclically reduced word are cyclically reduced again.
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.
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