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Page "Group scheme" ¶ 20
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Any and affine
* Any non-degenerate affine transformation takes a parallelogram to another parallelogram.
* Any coset of a subspace of a vector space is an affine space over that subspace.
Any affine scheme is separated, therefore any scheme is locally separated.
Any action of the group by continuous affine transformations on a compact convex subset of a ( separable ) locally convex topological vector space has a fixed point.
Any two affine parameters are linearly related.

Any and group
* Any member of the genus Eunectes, a group of large, aquatic snakes found in South America
Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.
Any formal or informal groupa family, a church, a club, a business, a trade union — may be said to have government.
* Any Lie group G defines an associated real Lie algebra.
* Any topologically closed subgroup of a Lie group is a Lie group.
* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.
# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
" Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.
Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.
However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).
* Any subgroup of a free group is free.
Any group of four students may run for office, but there must always be four students.
Any group that managed to find ways of reasoning effectively would reap benefits for all its members, increasing their fitness.
Any time during a triad conversation, group members can switch seats and one of the co-pilots can sit in the pilot ’ s seat.
Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.

Any and scheme
Any digital modulation scheme uses a finite number of distinct signals to represent digital data.
Any comprehensive scheme of accounting reform is a major professional and academic enterprise ; Typically it requires examination of the role of each of the fundamental factors of production, an analysis of capital indicating how many types there are and how each supports each factor of a production process.
Any additional enmity that would be earned from territorial concessions was downplayed as marginal and insignificant in the overall scheme of things.
Any scheme S has a unique morphism to Spec ( Z ), so this attitude, part of the relative point of view, doesn't lose anything.
Any group scheme admits natural left and right actions on its underlying scheme by multiplication and conjugation.
Any group scheme G of finite type is an extension of the connected component of the identity ( i. e., the maximal connected subgroup scheme ) by a constant group scheme.
Any complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type over a field ) is automatically commutative, by an argument involving the action of conjugation on jet spaces of the identity.
Any backup scheme has some labor requirement, but complicated schemes have considerably higher labor requirements.
Any Tibetan language romanization scheme is faced with a dilemma: should it seek to accurately reproduce the sounds of spoken Tibetan, or the spelling of written Tibetan?
Any editing application which supports NTSC video can be used to edit footage employing the 3: 2 pulldown scheme.
Any scheme he has in mind has the end result of getting him one of the two.
Any buyers of the stock who are unaware of the scheme become victims once the price falls.
Any decision taken under this scheme will require the support of at least 55 % of the Council of the European Union members who must also represent at least 65 % of the EU's citizens.
Any digital modulation scheme uses a finite number of distinct signals to represent digital data.
Any new scheme would use a smarycatd which would then be usable in-at least-all Dublin public transport systems.
Any compulsory scheme of data retention would also be affected by Article 8 ( the respect for the right of privacy ) of the European Convention on Human Rights.
Any reduced scheme has a normalization, whose construction we first give for irreducible reduced schemes.

Any and is
Any organism that falters or misperceives the signals or weakens is done.
Any information we have here in Taiwan is at your disposal ''.
Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.
Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.
Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.
Any action is understood to create " seeds " in the mind that sprout into the appropriate results ( Pāli vipaka ) when they meet the right conditions.
** Any union of countably many countable sets is itself countable.
Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.
Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.
Any word or phrase that exactly reproduces the letters in another order is an anagram.
Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.
" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.
Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.
Any person who is seen as a threat to civil aviation is banned from flying.
* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.
* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.
* Any commutative ring R is an algebra over itself, or any subring of R.
Any form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.
* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.

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