Examples of using Simple groups in English and their translations into Danish
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He also studied infinite series of finite simple groups.
The classification of finite simple groups involved contributions by a host of mathematicians world wide.
These results are the first substantial results achieved concerning simple groups.
The nonabelian finite simple groups fall into a small number of infinite series and 26 sporadic groups. .
Leech is, however, best known for the Leech lattice which gives rise to three sporadic simple groups.
He searched for finite simple groups and in an 1892 paper he showed that all simple groups up to order 200 are already known.
Every finite group can be viewed as built from a finite collection of finite simple groups.
Surely they were missing some geometric interpretation of the simple groups that would lead to a substantially shorter classification proof.
Brauer was to spend the rest of his life working on the problem of classifying the finite simple groups.
If is for the classification of finite simple groups that his name will always be remembered, certainly the mathematical achievement of the 20th century.
Thompson, working with Walter Feit,proved in 1963 that all nonabelian finite simple groups were of even order.
In On non-strictly simple groups published in 1963 Hall established the existence of simple groups which were the infinite union of a chain of subgroups, each normal in the next.
Leech died almost exactly one month after Gorenstein who had overseen 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.
Here, the authors proved a famous conjecture,to the effect that all non-cyclic finite simple groups have even order.
Another major early step by Thompson towards the classification of finite simple groups was his classification of those finite simple groups in which every soluble subgroup has a soluble normaliser.
I[EFR] cannot vouch for this change in confidence since I did not hear Conway lecture before his discovery of new simple groups.
In it he determined the minimal simple finite groups, this is to say, the simple groups whose proper subgroups are solvable.
The reason was that suddenly progress began to be made on one of the main problems of finite group theory,namely the classification of finite simple groups.
It had a great number of very interesting subgroups,including two more previously unknown simple groups, as well as groups having as homomorphic images almost all the finite sporadic simple groups known at that time.
This result stunned the world of mathematics butit also led mathematicians to believe that a classification of finite simple groups might prove possible.
Besides containing a discussion of the possible order types of abelian series in simple groups, the paper also presents an extremely informative survey of the inter-relations that are known or conjectured to exist between the various classes of generalized soluble groups. .
These groups play an important role in the classification of finite simple groups coordinated by Gorenstein.
He began to formulate a method to classify all finite simple groups andhis 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 and this did not appear in print until 1958.
This important piece of work is one of a number of results leading to the intense interest in finite simple groups which eventually led to their classification.
Conway in England, and Fischer in Germany, each discovering three new sporadic groups, stimulated considerable additional interest,leading to an intensification of the search for further simple groups.
Karl Gruenberg explains some further features of this paper:Besides containing a discussion of the possible order types of abelian series in simple groups, the paper also presents an extremely informative survey of the inter-relations that are known or conjectured to exist between the various classes of generalized soluble groups. .
He also used geometrical configurations to investigate groups and, although his work was out of fashion at a time when group theorists were moving towards the classification of finite simple groups, his work did provide a deeper understanding of some of these groups, for example Conway 's simple groups.
This is a simple group, nothing special.
A finite sporadic simple group is a finite simple group which is not a member of one of the standard infinite families.