CN group

In mathematics, in the area of algebra known as group theory, a more than fifty year effort was made to answer a conjecture of harv|Burnside|1911: are all groups of odd order solvable? Progress was made by showing that CA groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable harv|Suzuki|1957. Further progress was made showing that CN groups, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable harv|Feit|Hall|Thompson|1961. The complete solution was given in harv|Feit|Thompson|1963, but further work on CN groups was done in harv|Suzuki|1961, giving more detailed information about the structure of these groups. For instance, a non-solvable CN group "G" is such that its largest solvable normal subgroup "O"_∞("G") is a 2-group, and the quotient is a group of even order.

References

Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… … Wikipedia
Group psychotherapy — is a form of psychotherapy in which one or more therapists treat a small group of clients together as a group. The term can legitimately refer to any form of psychotherapy when delivered in a group format, including Cognitive behavioural therapy… … Wikipedia
Group dynamics — is the study of groups, and also a general term for group processes. Relevant to the fields of psychology, sociology, and communication studies, a group is two or more individuals who are connected to each other by social relationships. [Forsyth … Wikipedia
Group of death — is an informal sobriquet used in football and other team sports to describe a situation that often occurs during the group stage of a tournament (such as the first round of the World Cup), where:* all the teams present in one group are considered … Wikipedia
Group buying — Group buying, also known as collective buying, offers products and services at significantly reduced prices on the condition that a minimum number of buyers would make the purchase. Origins of group buying can be traced to China[citation needed]… … Wikipedia
group — [gruːp] noun [countable] 1. also group of companies ORGANIZATIONS a large business organization that consists of several companies that all have the same owner: • Burmah Castrol, the lubricants group • the sale of the Rover Group to BMW … Financial and business terms
Group — can refer to: Sociology * Group action (sociology) * Group behaviour * Groups of people, a description of various different human groups ** Peer group ** Workgroup * Group dynamics * Group (sociology), a sub set of a culture or of a society *… … Wikipedia
Group f/64 — was a group of famous San Francisco photographers who espoused a common philosophy and photographic style. The group was created in 1932, and it is usually listed as including: * Ansel Adams+ * Imogen Cunningham+ * John Paul Edwards+ * Consuelo… … Wikipedia
Gröûp X — (also known as Gröûp X: Arabian Rap Sensations) is a faux Arabian rock band, claiming to be from the fictional village of Cramshananteen, Saudi Arabia. They play a mix of rap and rock. They are known for using comically accented and mangled… … Wikipedia
Group polarization — is the tendency of people to make decisions that are more extreme when they are in a group as opposed to a decision made alone or independently. Overview Study of this effect has shown that after participating in a discussion group, members tend… … Wikipedia
Group marriage — Group marriage, also known as multi lateral marriage, is a form of polyamory in which more than two persons form a family unit, with all the members of the group marriage being considered to be married to all the other members of the group… … Wikipedia

Academic Dictionaries and Encyclopedias

CN group

Look at other dictionaries:

Share the article and excerpts

Academic Dictionaries and Encyclopedias

Wikipedia

CN group

Look at other dictionaries:

Share the article and excerpts

Direct link