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Page "Group scheme" ¶ 19
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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 affine group scheme is the spectrum of a commutative Hopf algebra ( over a base S, this is given by the relative spectrum of an O < sub > S </ sub >- algebra ).
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 affine scheme is separated, therefore any scheme is locally separated.
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 G
Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.
* Any two vertices in G can be connected by a unique simple path.
Unsigned, Mushroom ( Andy Vowles ), Daddy G ( Grant Marshall ) and 3D ( Robert Del Naja ) put out " Any Love " as a single, co-produced by Bristol double-act Smith & Mighty.
# Any group G may be regarded as an " abstract " category with one object,, and one morphism for each element of the group.
* Any open set is trivially a G < sub > δ </ sub > set
* Any principal bundle with structure group G gives a groupoid, namely over M, where G acts on the pairs componentwise.
* Any Lie group with an infinite group of components G / G < sup > o </ sup > cannot be realized as an algebraic group ( see identity component ).
* Any group G can be considered as a one-object category in which every morphism is invertible.
A graph coloring is an assignment of one of k colors to a graph G so that the endpoints of each edge have different colors, for some number k. Any coloring corresponds to a homomorphism from G to a complete graph K < sub > k </ sub >: the vertices of K < sub > k </ sub > correspond to the colors of G, and f maps each vertex of G with color c to the vertex of K < sub > k </ sub > that corresponds to c. This is a valid homomorphism because the endpoints of each edge of G are mapped to distinct vertices of K < sub > k </ sub >, and every two distinct vertices of K < sub > k </ sub > are connected by an edge, so every edge in G is mapped to an adjacent pair of vertices in K < sub > k </ sub >.
Any canonical transformation involving a type-2 generating function G < sub > 2 </ sub >( q, P, t ) leads to the relations
Let now v and w be two vertices in G. Any spanning tree contains precisely one simple path between v and w. Taking this path in the uniform spanning tree gives a random simple path.
** Any parabolic element of G fixing a boundary point of D is in H.
( 2 ) Any sequence of continuous positive definite functions on G converging to 1 uniformly on compact subsets, converges to 1 uniformly on G.

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