[permalink] [id link]
For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.
from
Wikipedia
Some Related Sentences
For and every
For every criterion which defines what something is, at the same time proclaims -- implicitly if not openly -- what that something is not.
For new galaxies to be created, Professor Bondi declares, it would only be necessary for a single hydrogen atom to be created in an area the size of your living room once every few million years.
For example, " biweekly " can mean " fortnightly " ( once every two weeks – 26 times a year ), or " twice a week " ( 104 times a year ).
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.
For Tarrou, plague is the destructive impulse within every person, the will and the capacity to do harm, and it is everyone's duty to be on guard against this tendency within themselves, lest they infect someone else with it.
For Hume, every effect only follows its cause arbitrarily — they are entirely distinct from one another.
Professor Henry Higgins sings, " Look at her, a prisoner of the gutters / Condemned by every syllable she utters / By right she should be taken out and hung / For the cold-blooded murder of the English tongue.
For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.
For example, the BBC website, which had previously been called BBC Online, took on the BBCi brand from 2001, displaying an i-bar across the top of every page, offering a category-based navigation: Categories, TV, Radio, Communicate, Where I Live, A-Z Index, and a search.
For example, in the Schrödinger picture, there is a linear operator U with the property that if an electron is in state right now, then in one minute it will be in the state, the same U for every possible.
For and group
For it includes the emotional ties that bind men to their homeland and the complex motivations that hold a large group of people together as a unit.
For ten years a small group of European and U.S. critics has been calling attention to the half-forgotten Austrian expressionist Egon Schiele, who died 42 years ago at the age of 28.
For example, the steering committee might announce that the group felt a topic under study should not be dropped for an additional week as there was still too much of it untouched.
For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.
For if the small group notion involves the implicit claim that the phenomena of sociological investigations are of atomic or subatomic proportions, the philosopher needs to know the extent to which such entities are valid.
For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.
For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G → G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).
For example, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other ( ortho ), one position removed from each other ( meta ), or two positions removed from each other ( para ).
For the U. S. Government's scientific enterprise, a significant impact of NAPAP were lessons learned in the assessment process and in environmental research management to a relatively large group of scientists, program managers and the public.
For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
For a few years, this group of animals was regarded as a subfamily, called the Callitrichinae, of the family Cebidae.
For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">
For example, an " X " is used to indicate a variable group amongst a class of compounds ( though usually a halogen ), while " R " is used for a radical, meaning a compound structure such as a hydrocarbon chain.
For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">
For example, it is immediately proven from the axioms that the identity element of a group is unique.
For and G
For loan to the Government of India under subsection ( G ) of Section 104 of the Act, the rupee equivalent of not more than $538 million for financing such projects to promote balanced economic development as may be mutually agreed.
For example the United States uses NTSC-M, the UK uses PAL-I, France uses SECAM-L, much of Western Europe and Australia uses PAL-B / G, most of Eastern Europe uses PAL-D / K or SECAM-D / K and so on.
For example " GOOD DOG " can be encrypted as " PLLX XLP " where " L " substitutes for " O ", " P " for " G ", and " X " for " D " in the message.
For any topological space X the ( Alexandroff ) one-point compactification αX of X is obtained by adding one extra point ∞ ( often called a point at infinity ) and defining the open sets of the new space to be the open sets of X together with the sets of the form G < font face =" Arial, Helvetica "> U </ font >
for some natural number n. Moreover, since, the commutator subgroup is normal in G. For any homomorphism f: G → H,
groups ( G, *) and ( H, ●), denoted by G × H. For abelian groups which are written additively, it may also be called the direct sum of two groups, denoted by.
For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.
For their part, the Italians developed several monoplanes such as the Fiat G. 50, but being short on funds, were forced to continue operating obsolete Fiat CR. 42 biplanes.
For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re-added, the four-coloring can be extended to it as well.
0.176 seconds.