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 path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.

Every man in every one of these houses is a Night Rider.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

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 retraction is an epimorphism, and every section is a monomorphism.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed.

Every mental phenomenon, every psychological act, has a content, is directed at an object ( the intentional object ).

Every step had been carefully planned, every calculation meticulously done.

" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

Every valley, every cliff, to my look is beautiful.

Every seminorm on V ( in particular, every norm on V ) is sublinear.

Every little change in every little property would mean the whole thing is destroyed.

Every few minutes she would awaken for a moment to review things: Stowey, yes, was on his way south, and the two boys were away in school, and nothing was burning on the stove, and Lucretia was coming for dinner and bringing three guests of hers.

`` Every month, f'r three days '', he said happily, `` I take no water into my system, no water whatsoever.

Every week Holbrook writes the story line for the next three weeks for one of his strips and draws the next three weeks ' worth of strips for another.

* Every three years since Earnhardt's death, someone associated with Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr. in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010.

Every January 19, in the early hours of the morning, the person made a toast of cognac to Poe's original grave marker and left three roses.

Every point in three-dimensional Euclidean space is determined by three coordinates.

Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".

Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.

From a pro-independence supporter's point of view, the movement for Taiwan independence began under Qing rule in the 1680s which led to a well known saying those days, " Every three years an uprising, every five years a rebellion ".

Every island has one or two short airstrips where Vanair ’ s Twin Otter planes land two or three times weekly.

Every three years, member nations that provide funds to the IDA gather together to replenish the IDA's resources.

However, the three propositions have different domains: the first proposition says something about " Every object ", while the second says something about " Every raven ".

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.

: Every integer greater than 2 can be written as the sum of three primes.

: Every integer greater than 5 can be written as the sum of three primes.

They draw three conclusions from Austin: ( 1 ) A performative utterance does not communicate information about an act second-hand — it is the act ; ( 2 ) Every aspect of language (" semantics, syntactics, or even phonematics ") functionally interacts with pragmatics ; ( 3 ) There is no distinction between language and speech.

Every three to four years, the CSUCS publishes the " Child Soldiers Global Report ".

Every night for three years, she undoes part of the shroud, until Melantho, one of twelve unfaithful serving women, discovers her chicanery and reveals it to the suitors.

In the autumn of 1970 Jurgen Wischnewski of the SPD declared, ‘ Every week more than three plans for reform come up for decision in cabinet and in the Assembly .’ ”

Every three months, it publishes a technology report called Technology Quarterly or TQ.

Every three months, it publishes a " Technology Quarterly ," a special section focusing on recent trends and developments in science and technology.

Every two years all eight districts of one of those groups elect all their three senators, assigning two of them from the party that obtains the majority, and one from the first minority party.