Examples of using Finite simple groups in English and their translations into Hungarian
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Finite simple groups.
History for finite simple groups.
A major undertaking in20th century mathematics was to classify the finite simple groups.
The Finite Simple Groups.
The Status of the Classification of the Finite Simple Groups.
List of finite simple groups.
Brauer was to spend therest of his life working on the problem of classifying the finite simple groups.
There are 18 infinite families of finite simple groups plus 26 exceptional sporadic groups. .
The finite simple groups are therefore the building blocks from which finite groups are built.
Here, the authors proved a famous conjecture,to the effect that all non-cyclic finite simple groups have even order.
The nonabelian finite simple groups fall into a small number of infinite series and 26 sporadic groups. .
Thompson, working with Walter Feit, proved in 1963 that all nonabelian finite simple groups were of even order.
He searched for finite simple groups and in an 1892 paper he showed that all simple groups up to order 200 are already known.
Claude Chevalley showed in 1955 that the Liegroups have finite analogues which are finite simple groups.
Brauer had announced these results and his programme for classifying finite simple groups at the International Congress of Mathematicians in Amsterdam in 1954.
One of the greatest achievements oftwentieth century mathematics was the classification of all finite simple groups.
This he used to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work.
The reason was that suddenly progress began tobe made on one of the main problems of finite group theory, namely the classification of finite simple groups. .
The Schreier conjecture, that the outer automorphism groups of finite simple groups are soluble, was shown to be true as a consequence of the classification of finite simple groups. .
Most important was Brauer's vital step in setting the direction for the whole classification programme in the paper On groups of even order where itis shown that there are only finitely many finite simple groups containing an involution whose centraliser is a given finite group.
Another major early step by Thompson towards the classification offinite simple groups was his classification of those finite simple groups in which every soluble subgroup has a soluble normaliser.
He began to formulate a method to classify all finite simple groups and his first step on this road was a group-theoretical characterisation of the simple groups PSL(2,q) in 1951(although for a complicated number of reasons explained in[6] and[1] this did not appear in print until 1958).
To classify finite groups therefore reduces to two problems, namely the classification of finite simple groups and the solution of the extension problem, that is the problem of how to fit the building blocks together.
Then in 1967 Higman became interested in the sporadic finite simple groups being discovered at this time and played an important role in constructing certain of these groups from a knowledge of their character tables.
Every finite simple group can be generated by two elements!
The paper was On groups of even order and it provided the key to the major breakthrough by Walter Feit andJohn Thompson when they proved that every finite simple group has even order.
In it he determined the minimal simple finite groups, this is to say, the simple groups whose proper subgroups are solvable.
Of simple finite groups.