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A group action is an extension to the definition of a symmetry group in which every element of the group " acts " like a bijective transformation ( or " symmetry ") of some set, without being identified with that transformation.
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group and action
The action centers about a group of outspoken and offbeat students sitting around a table in a cafeteria and their collective and ultimately fruitless search for a cup of hot coffee.
Specific differences exist in the action of different drugs belonging to the same group as, for instance, between reserpine and chlorpromazine.
Spoilage by chemical action results from the reaction of one group of components in the food with others or with its environment, as in corrosion of the walls of metal containers or the reaction of fats with oxygen in the air to produce rancidity.
Karma is categorized within the group or groups of cause ( Pāli hetu ) in the chain of cause and effect, where it comprises the elements of " volitional activities " ( Pali sankhara ) and " action " ( Pali bhava ).
Additionally, consider for instance the unit circle S, and the action on S by a group G consisting of all rational rotations.
Such tasks, which usually required a coordinated group effort in either a pulling or pushing action, included weighing anchor and setting sail.
Advertising is a form of communication for marketing and used to encourage or persuade an audience ( viewers, readers or listeners ; sometimes a specific group ) to continue or take some new action.
On 15 August 1909 the Military League, a group of Greek officers, took action against the government to reform their country's national government and reorganize the army.
In fact, the purpose of Critical Mass is not formalized beyond the direct action of meeting at a set location and time and traveling as a group through city streets.
The final Italian cavalry action occurred on October 17, 1942 in Pola ( Croatia ) by a squadron of " Alexandria Cavalry Regiment " against a large group of Yugoslav partisans.
In law, a class action, a class suit, or a representative action is a form of lawsuit in which a large group of people collectively bring a claim to court and / or in which a class of defendants is being sued.
The ancestor of the class action was what modern observers call " group litigation ," which appears to have been quite common in medieval England from about 1200 onward.
Just as medieval group litigation bound all members of the group regardless of whether they all actually appeared in court, the modern class action binds all members of the class, with the exception of those who appear and object.
In a class action, the plaintiff seeks court approval to litigate on behalf of a group of similarly-situated persons.
In this view expertise is socially constructed ; tools for thinking and scripts for action are jointly constructed within social groups enabling that group jointly to define and acquire expertise in some domain.
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.
Although political freedom is often interpreted negatively as the freedom from unreasonable external constraints on action, it can also refer to the positive exercise of rights, capacities and possibilities for action, and the exercise of social or group rights.
group and is
The content is not the same, however: rather than individual security, it is the security and continuing existence of an `` ideological group '' -- those in the `` free world '' -- that is basic.
Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.
The music director of the Pittsburgh Symphony Orchestra, William Steinberg, has molded his group into a prominent musical organization, which is his life.
With the group of boys it is different.
Nothing is more revealing of the way of life and literary aspirations of this group than their attitude toward sex.
This group is secularist and their program tends to be technological.
But the problem is one which gives us the measure of a man, rather than a group of men, whether a group of doctors, a group of party members assembled at a dinner to give their opinion, or the masses of the voters.
The group conducting the review is not holding formal hearings.
After allowing for group exposures, it is apparent that other factors must be considered if we are to comprehend fanaticism.
At Sounion there is a group of beautiful columns, the ruins of a temple to Poseidon, of particular interest at that time, as active reconstruction was in progress.
He is uncompromising in assigning guilt to the man who finds it necessary to inflict or permit injury to one individual or group for the sake of a larger good.
In the main stream of historical thinking is a group of scholars, H.M. Chadwick, R.H. Hodgkin, Sir Frank Stenton et al. who are in varying degrees sceptical of the native traditions of the conquest but who defend the catastrophic type of invasion suggested by them.
Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.
Patchen's musicians are outsiders in established jazz circles, and Patchen himself has remained outside the San Francisco poetry group, maintaining a self-imposed isolation, even though his conversion to poetry-and-jazz is not as extreme or as sudden as it may first appear.
Gov. Dalton's New Commerce and Industry Commission is moving to create a nine-state regional group in a collective effort to attract new industry.
Fortunately, there is a nursery school which he has been able to attend, with a group of normal children.
Perhaps Khrushchev is in a more difficult position than any since 1957, when the `` anti-party group '' nearly liquidated him.
When the fate of the individual is visited on the group, then ( the warm sweet butter dripped from her raised trembling fork and she pushed her head forward belligerently ), ah, then the true bitterness of existence could be tasted.
Mr. Claude is a specialist in torso development and he has long favored the now-famous Weider Push-Pull Super-Set technique in which one exercise of the Super-Set is a pressing or `` pushing '' movement which accents one sector of a muscle group in a specific way, followed by a `` pulling '' exercise which works the opposing sector of the same muscle group.
group and extension
In the case of a Galois extension L / K the subgroup of all automorphisms of L fixing K pointwise is called the Galois group of the extension.
By extension, it has come to include an extreme and unreasoning partisanship on behalf of any group to which one belongs, especially when the partisanship includes malice and hatred towards rival groups.
So to classify these groups one takes every central extension of every known finite simple group, and finds all simple groups with a centralizer of involution with this as a component.
Bartov commented that in this film, the German officer corps is shown as a group of fundamentally noble and civilized men who happened to be serving an evil regime made up of a small gang of gangsterish misfits totally unrepresentative of German society, which served to exculpate both the officer corps and by extension Germany society.
In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
If E / F is a Galois extension, then Aut ( E / F ) is called the Galois group of ( the extension ) E over F, and is usually denoted by Gal ( E / F ).
The significance of an extension being Galois is that it obeys the fundamental theorem of Galois theory: the closed ( with respect to the Krull topology below ) subgroups of the Galois group correspond to the intermediate fields of the field extension.
If E / F is a Galois extension, then Gal ( E / F ) can be given a topology, called the Krull topology, that makes it into a profinite group.
Mies found appeal in the use of simple rectilinear and planar forms, clean lines, pure use of color, and the extension of space around and beyond interior walls expounded by the Dutch De Stijl group.
* Some totally disconnected groups, such as the Galois group of an infinite extension of fields, or the additive group of the p-adic numbers.
Specifically, if L / K is a Galois extension, we consider the group G = Gal ( L / K ) consisting of all field automorphisms of L which keep all elements of K fixed.
This group is the inverse limit of the finite groups Gal ( F / K ), where F ranges over all intermediate fields such that F / K is a finite Galois extension.
In 2003, the Vienna group also demonstrated the wave nature of tetraphenylporphyrin — a flat biodye with an extension of about 2 nm and a mass of 614 u.
The extension of an object in abstract algebra, such as a group, is the underlying set of the object.
The Krishi Vigyan Kendra, Kannur under Kerala Agricultural University has developed an innovative extension approach called compact area group approach ( CAGA ) to combat coconut mites.
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