Fundamental group: Consider the category of pointed topological spaces, i. e. topological spaces with distinguished points.

< li > Consider the group ( Z < sub > 6 </ sub >, +), the integers from 0 to 5 with addition modulo 6.

Consider the category Grp of all groups with group homomorphisms as morphisms.

Consider the category Ab of abelian groups and group homomorphisms.

Consider the possibility of creating an ' artificial ' structure to group some otherwise unrelated, but nevertheless frequently referenced, items together.

Consider a periodic group G with the additional property that there exists a single integer n such that for all g in G, g < sup > n </ sup >

Consider the direct system composed of the groups Z / p < sup > n </ sup > Z and the homomorphisms Z / p < sup > n </ sup > Z → Z / p < sup > n + 1 </ sup > Z which are induced by multiplication by p. The direct limit of this system consists of all the roots of unity of order some power of p, and is called the Prüfer group Z ( p < sup >∞</ sup >).

Consider in a vector space V, the general linear group GL ( V ).

Consider the positive real numbers R < sup >+</ sup >, a Lie group under the usual multiplication.

Consider a large group of items in which a very few are different in a particular way ( for e. g. Defective products or infected test subjects ).

Consider, for example, the construction of the free group in two generators.

Consider a finite group G, a field k and the group algebra kG.

Consider a group of N separate Dp-branes, arranged in parallel for simplicity.

Consider the comparison to its RCOOH acid analogue: the chloride ion is an excellent leaving group while the hydroxide is not under normal conditions ; i. e. even weak nucleophiles attack the carbonyl.

Consider the unit circle S, and the action on S by a group G consisting of all rational rotations.

Consider a finite group permuting those indeterminates over K. By standard Galois theory, the set of fixed points of this group action is a subfield of, typically denoted.

Consider for example the dihedral group D < sub > 4 </ sub > of symmetries of a square.

Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots.

Consider the tensor product of modules H < sub > i </ sub >( X, Z ) ⊗ A. The theorem states that there is an injective group homomorphism ι from this group to H < sub > i </ sub >( X, A ), which has cokernel Tor ( H < sub > i-1 </ sub >( X, Z ), A ).

Consider singular cohomology with coefficients in an abelian group A.

Consider a ( multiplicative ) cyclic group of order, and with generator.

* P. J. Rudall, K. L. Stobart, W .- P. Hong, J. G. Conran, C. A. Furness, G. C. Kite, M. W. Chase ( 2000 ) Consider the Lilies: Systematics of Liliales.

Consider all the functions φ: G → R such that the set

* Winterton, G, ' Should the High Court Consider Policy?

Consider a graph G with vertices V, each numbered 1 through N. Further consider a function shortestPath ( i, j, k ) that returns the shortest possible path from i to j using vertices only from the set

Consider the matrix A = A ( G ) whose matrix elements are where is the kth element of G.

Consider a classically parity-invariant gauge theory whose gauge group G has dual coxeter number h in 3-dimensions.

They are maps from flat 3-space into the Lie group G. Consider now glueing these two balls together at their boundary S².

Consider a cyclic group G of order q.

Consider a group G acting on a set X.

Consider the space X < sup > 1 </ sup >( G ) consisting of restrictions to G of C < sup > 1 </ sup > vector fields on R < sup > n </ sup > that are transversal to the boundary of G and are inward oriented.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

Let H be a Hilbert space and L ( H ) the bounded operators on H. Consider a self-adjoint subalgebra M of L ( H ).

This task also requires resource R. Consider H starts after L has acquired resource R. Now H has to wait until L relinquishes resource R.

Consider the Poincaré half-plane model H of 2-dimensional hyperbolic geometry.

Consider, for example, the behavior of water ( the molecule H < sub > 2 </ sub > O ) which, depending on temperature and pressure, naturally exists in just one of three states: gas, liquid or ice.

Consider a continuous linear operator A: H → H ( this is the same as a bounded operator ).

Consider an ensemble of systems described by a Hamiltonian H with average energy E. If H has pure-point spectrum and the eigenvalues of H go to + ∞ sufficiently fast, e < sup >- r H </ sup > will be a non-negative trace-class operator for every positive r.

Consider a mixture of one mole of ethane ( C < sub > 2 </ sub > H < sub > 6 </ sub >) and one mole of oxygen ( O < sub > 2 </ sub >).

* Consider the set K of all functions ƒ: → satisfying the Lipschitz condition | ƒ ( x ) − ƒ ( y )| ≤ | x − y | for all x, y ∈.

Consider on K the metric induced by the uniform distance.

* Consider the field K = Q ( ³ √ 2 ).

Consider a system of K wire loops, each with one or several wire turns.

Consider a call option and a put option with the same strike K for expiry at the same date T on some stock S, which pays no dividend.

Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad ( x ) ( also written as ad < sub > x </ sub >) of g with the help of the Lie bracket, as

Consider the field K