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Page "Elementary group theory" ¶ 24
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Given and left
Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.
Given the harsh conditions of the retreat, the infant was left with a local family ( Two Europeans retracing the Long March route in 2003 met a woman in rural Yunnan province, said by local officials to be Mao and He Zizhen's long-lost daughter ).
Given glam metal's lack of a major format presence on radio, bands were left without a clear way to reach their audience.
Given the homogeneity of the fluid, the bulk of the particles do not experience a net force pulling them to the right or to the left.
Given the innately rich and personal world of fantasy he has left himself locked into, Morgan goes off the deep end, enacting a series of bizarre stunts in a campaign to win Leonie back, including putting a skeleton in her bed and crashing her wedding dressed as a gorilla, for which scene Reisz borrows clips from from the original King Kong film to illustrate Morgan's fantasy world.
Given the SLP's stance on the left, Sillars was naturally in line with the 79 Group's policy and immediately joined it too.
Given the Nizam's determination not to join India, this left Hyderabad as an independent country.
Given the proximity of the jewel keeper's domestic quarters to the site of the commotion, Edwards ' wife invited them upstairs to their apartment to recover, after which Blood and his wife thanked the Edwardses and left.
For a finite group G, the left regular representation λ ( over a field K ) is a linear representation on the K-vector space V whose basis is the elements of G. Given g ∈ G, λ ( g ) is the linear map determined by its action on the basis by left translation by g, i. e.
Given the dwindling support for the NDP reflected in all the public opinion polls, the formation of a new party on the left could not be ignored.
# Given a slab subdivided into regions by non-intersecting segments that completely cross the slab from left to right, determine which region contains a given point.
The news was disappointing for Newcastle fans who felt that Given left the club in a poor situation with many thinking that had Given delayed his decision to leave until the summer then Newcastle would have subsequently survived relegation to the Championship because Given was such a fantastic goal keeper who could have stopped many of the goals that the Toon conceded towards the end of the dreadful campaign.
Given of a monoid M of every strings over some alphabet, one may define sets that consist of formal left or right inverses of elements in S. These are called quotients, and one may define right or left quotients, depending on which side one is concatenating.
Given the costs of the road improvements, the monument itself besides the splendid funeral, and that the corporation it seems did not match a penny to these expenses having control of the Surfboat-men s money, it is a lamentable indictment to Thanet s officials that although their still should have been money enough left over, had it been wisely invested, to have yielded an income for life to the widows and orphans, who in the end personally received nothing out of the fund.
Given that the ESCP is a regulation and not a directive, it is arguable whether it has left too many aspects to the discretion of member states, which could call into question the legal certainty expected from a European regulation.
Given this dire prognosis, he left the hat-making business to explore the American West, afraid this would be his only chance to see it.
Let M be a ( left or right ) module over some ring R. Given a chain of submodules of M of the form
Given no other choice, Kolish contacted his only remaining adult relative, a brother who lived in Hollywood, and left instructions for the care of Sarria and his family.
Given police permission to search Sobhraj's apartment ( a full month after the suspect had left the country ), Knippenberg found much evidence, such as victims ' documents and poison-laced medicines.
Given that her lord's kinsmen ( þæt monnes magas ) are described as taking measures to separate the speaker from him, a probable interpretation of the speaker's initial circumstances is that she has been entered into an exogamous relationship typical within the Anglo-Saxon heroic tradition, and her marital status has left her isolated among her husband's people, who are hostile to her, whether due to her actions or merely due to political strife beyond her control.

Given and neutral
Given a small angular displacement, the vessel may return to its original position ( stable ), move away from its original position ( unstable ), or remain where it is ( neutral ).
Given its heritage, MCC continues to participate in the administration of English cricket, and in 2010 offered Lord's as a neutral venue for Pakistan to stage a " home " Test match, as scheduled by the ICC, versus Australia ; although the outcome of that game proved controversial the club's initial offering was made with the intention that Pakistan, whose terrorist-stricken country had rendered it a no-go area for international cricket, could remain within the international cricketing fold.

Given and element
: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.
Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).
Given a set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.
* Given a binary operation, an idempotent element ( or simply an idempotent ) for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result.
Given a binary operation ★ on a set S, an element x is said to be idempotent ( with respect to ★) if
Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors.
Given an element φ of H *, the orthogonal complement of the kernel of φ is a one-dimensional subspace of H. Take a non-zero element z in that subspace, and set.
Given a natural transformation Φ from h < sup > A </ sup > to F, the corresponding element of F ( A ) is.
# Given any element a of G, a ~ a ( reflexivity );
: Given any set A, there is a set B such that, for any element c, c is a member of B if and only if there is a set D such that c is a member of D and D is a member of A.
Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.
Given any group G, the group consisting of only the identity element is a trivial group and being a subgroup of G is called the trivial subgroup of G.
Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.
Given a function and an element g ∈ G,
* Given a maximal torus T in G, every element g ∈ G is conjugate to an element in T.
Given an integral domain, let be an element of, the polynomial ring with coefficients in.
Given an element of a disjoint union A + B, it is possible to determine whether it came from A or B.
Given then a normal extension L of K, with automorphism group Aut ( L / K ) = G, and containing α, any element g ( α ) for g in G will be a conjugate of α, since the automorphism g sends roots of p to roots of p. Conversely any conjugate β of α is of this form: in other words, G acts transitively on the conjugates.
Given a partially ordered class P, we can form a category with P's elements as objects and a single arrow going from one object ( element ) to another if the first is less than or equal to the second.
Given a cyclic group of order, a generator of the group and a group element, the problem is to find an integer such that
Given a subset A of G, the measure can be thought of as answering the question: what is the probability that a random element of G is in A?

1.004 seconds.