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For general groups, Cauchy's theorem guarantees the existence of an element, and hence of a cyclic subgroup, of order any prime dividing the group order ; Sylow's theorem extends this to the existence of a subgroup of order equal to the maximal power of any prime dividing the group order.
Some Related Sentences
For and general
For many years a state tax on cities and towns was paid by the several municipalities to the state from the proceeds of the general property tax.
For the policy officer will know that action can almost never be secret and that in general the effectiveness of policy will be conditioned by the readiness of the country to sustain it.
For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;
For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.
For many of these unwed mothers, the data on their family life and early childhood experiences revealed several indications and sources of their basic mistrust of their parents in particular and of the world in general.
-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.
For general morale reasons and to encourage the efforts of his supply officers, when food was short for combat troops he cut the rations of his headquarters staff accordingly.
For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.
For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.
For biologists, this includes human beings, although for the general public the term " animal " means only non-human animals.
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 Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").
For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.
For example, if James's will states that he is leaving $ 500, 000 to his son Sam then the money would be a general devise.
For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.
For this reason, players should choose badminton shoes rather than general trainers or running shoes, because proper badminton shoes will have a very thin sole, lower a person's centre of gravity, and therefore result in fewer injuries.
For many years, the U. S. has borrowed and bought while in general, the rest of the world has lent and sold.
For several decades from the 1970s to early 2000s, the focus in designing high performance general purpose CPUs was largely on achieving high ILP through technologies such as pipelining, caches, superscalar execution, out-of-order execution, etc.
For example, the Napoleonic code expressly forbade French judges from pronouncing general principles of law.
For example, the copyright to a Mickey Mouse cartoon restricts others from making copies of the cartoon or creating derivative works based on Disney's particular anthropomorphic mouse, but does not prohibit the creation of other works about anthropomorphic mice in general, so long as they are different enough to not be judged copies of Disney's.
For many decades, consciousness as a research topic was avoided by the majority of mainstream scientists, because of a general feeling that a phenomenon defined in subjective terms could not properly be studied using objective experimental methods.
For and groups
( 3 ) For anionics, these micelles appear to be roughly spherical assemblages in which the hydrocarbon tails come together so that the polar groups ( the ionized ends ) face outward towards the aqueous continuous phase.
For they considered the odd numbers as male and the even ones as female, equating the two groups with the Yang and Yin principles in Nature ; ;
For a number of years, Wesleyan has been drawing varied groups of political and business leaders into these informal discussions with members of the faculty and student body, attempting to explore and clarify aspects of their responsibility for public policy.
For example, of the isomers of butene, the two methyl groups of ( Z )- but-2-ene ( aka cis-2-butene ) face the same side of the double bond, and in ( E )- but2-ene ( aka trans-2-butene ) the methyl groups face the opposite side.
For example, there are differences between African, East Asian and Indo-racial groups in how they metabolize alcohol.
For example, in organic chemistry chemists are sometimes concerned only with the functional groups of the molecule.
For many years, conservative parties fought to stop extension of voting rights to groups such as to non-Christians, non-whites and women.
( For groups of low 2-rank the proof of this breaks down, because theorems such as the signalizer functor theorem only work for groups with elementary abelian subgroups of rank at least 3.
; Security: For security reasons, it is desirable to limit who can see or change specific attributes or groups of attributes.
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, Lancaster students, motivated to save scrip, ultimately rented individual pages of textbooks from the school library, and read them in groups around music stands to reduce textbook costs.
For example Major General Charles J. Dunlap, Jr. says that United States Air Force culture includes an egalitarianism bred from officers as warriors who work with small groups of enlisted airmen either as the service crew or onboard crew of their aircraft.
For instance, although an individualist according to Cultural Theory is aversive towards both principles and groups, individualism is not fulfilling if individual brilliance cannot be recognised by groups, or if individual brilliance cannot be made permanent in the form of principles.
For all Abelian groups there is at least the automorphism that replaces the group elements by their inverses.