Примери за използване на Permutation groups на Английски и техните преводи на Български
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He studied primitive permutation groups and proved a finiteness theorem.
One of the areas which his work took him into was infinite permutation groups.
In it he considered permutation groups whose elements are determined by the images of three points.
Wielandt's research work continued on finite groups and on permutation groups.
The work on permutation groups led me inevitably to involvement with the structure theory of finite groups. .
It is to one of Schur's seminars that I owe the stimulus to work with permutation groups, my first research area.
It was on the topic of permutation groups that Wielandt wrote his doctoral dissertation and he was awarded a doctorate in 1935.
As a researcher, Kaluznin is best known for his work in group theory andin particular permutation groups.
In his doctoral dissertation of 1934 he considered permutation groups whose elements are determined by the images of three points.
He also gave several important theoremsin complex analysis and initiated the study of permutation groups.
Pólya's work using generating functions and permutation groups to enumerate isomers in organic chemistry was of fundamental importance.
He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra.
In fact Cauchy had written a major work on permutation groups between 1813 and 1815 and in it he generalised some of Ruffini's results.
He defined continuity in terms of infinitesimals and gave several important theorems in complex analysis andinitiated the study of permutation groups in abstract algebra.
Paolo Ruffini was the first person to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations.
As a researcher, Kaluznin is best known for his work in group theory and in particular permutation groups.
It started as the theory of permutation groups, but now the general theory of groups does not suppose that elements of groups should be permutations. .
Ruffini is the first to introduce the notion of the order of an element, conjugacy,the cycle decomposition of elements of permutation groups and the notions of primitive and imprimitive.
Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose.
Cauchy was asked to report on the work, which studied subgroups of low index in the symmetric group, andit clearly led him to return to study permutation groups himself.
He gives the'Cayley tables' of some special permutation groups but, much more significantly for the introduction of the abstract group concept, he realised that matrices and quaternions were groups. .
During these years hedevoted most of his time to his students, to his research activity on permutation groups, and to his newly cultivated interest in computer algebra.
He also considered permutation groups of small degree, groups having a small number of conjugacy classes, multiply transitive groups, and characteristic subgroups of finite groups. .
In 1884 he published his next paper on finite groups in which he proved Sylow's theorems for abstract groups(Sylow had proved his theorem as a result about permutation groups in his original paper).
At that time the only known groups were permutation groups and even this was a radically new area, yet Cayley defines an abstract group and gives a table to display the group multiplication.
This is, in essence, the first result in the theory of symmetric functions(beyond the basic building blocks which appeared in Chapter 1), a theory whose systematic development was not to appear until the 19th century(Lagrange, Gauss, and others) andwas ultimately followed by the theory of permutation groups(Galois, Jordan,…).
His book brought permutation groups into a central role in mathematics and, until Burnside wrote his famous group theory text nearly 30 years later, this work provided the foundation on which the whole subject was built.
After working on finitely generated nilpotent groups andinfinite simple permutation groups, Higman, together with Philip Hall, produced another of his landmark papers in 1956 On the p-length of p-soluble groups and reduction theorems for Burnside's problem.
Or the degree of a representation as a permutation group.
Netto made major steps towards abstract group theory when he combined permutation group results and groups in number theory.