3-step Group
In mathematics, a 3-step group is a special sort of group of Fitting length at most 3, that is used in the classification of CN groups and in the Feit–Thompson theorem In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by . History conjectured that every nonabelian finite simple group has even order. suggested using .... The definition of a 3-step group in these two cases is slightly different. CN groups In the theory of CN groups, a 3-step group (for some prime ''p'') is a group such that: * * is a Frobenius group with kernel * is a Frobenius group with kernel Any 3-step group is a solvable CN-group, and conversely any solvable CN-group is either nilpotent, or a Frobenius group, or a 3-step group. Example: the symmetric group ''S''4 is a 3-step group for the prime . Odd order groups defined a three-step group to be a group ''G'' satisfying the following conditions: *The der ...
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Fitting Length
In mathematics, specifically in the area of algebra known as group theory, the Fitting length (or nilpotent length) measures how far a solvable group is from being nilpotent. The concept is named after Hans Fitting, due to his investigations of nilpotent normal subgroups. Definition A Fitting chain (or Fitting series or ) for a group is a subnormal series with nilpotent quotients. In other words, a finite sequence of subgroups including both the whole group and the trivial group, such that each is a normal subgroup of the previous one, and such that the quotients of successive terms are nilpotent groups. The Fitting length or nilpotent length of a group is defined to be the smallest possible length of a Fitting chain, if one exists. Upper and lower Fitting series Just as the upper central series and lower central series are extremal among central series, there are analogous series extremal among nilpotent series. For a finite group ''H'', the Fitting subgroup ''Fit''(''H' ...
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CN Group
CN Group Limited was formerly an independent local media business based in Carlisle, Cumbria, England, operating in print and radio. It is now owned by Newsquest and their newspapers are printed in Glasgow. The company was formerly known as the Cumbrian Newspapers Group Ltd but changed its name to reflect the fact that is no longer primarily a newspaper publisher. One of its principal subsidiaries, however, is still known as Cumbrian Newspapers Ltd. History The company can trace its origins to the founding of the ''Carlisle Patriot'' newspaper in 1815, which eventually became the ''Cumberland News''. Historical copies of the ''Carlisle Patriot'', dating back to 1817, are available to search and view in digitised form at The British Newspaper Archive. Radio Until 2017 CN Group owned two radio stations: Lancaster-based The Bay and Kendal-based Lakeland Radio. In October 2017 it was announced that both had been sold to the UK media company Global. The company formerly owned ...
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Feit–Thompson Theorem
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by . History conjectured that every nonabelian finite simple group has even order. suggested using the centralizers of involutions of simple groups as the basis for the classification of finite simple groups, as the Brauer–Fowler theorem shows that there are only a finite number of finite simple groups with given centralizer of an involution. A group of odd order has no involutions, so to carry out Brauer's program it is first necessary to show that non-cyclic finite simple groups never have odd order. This is equivalent to showing that odd order groups are solvable, which is what Feit and Thompson proved. The attack on Burnside's conjecture was started by , who studied CA groups; these are groups such that the Centralizer of every non-trivial element is Abelian. In a pioneering paper he showed that all CA groups of odd order are ...
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Pacific Journal Of Mathematics
The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisation, and the University of California, Berkeley. It was founded in 1951 by František Wolf and Edwin F. Beckenbach and has been published continuously since, with five two-issue volumes per year and 12 issues per year. Full-text PDF versions of all journal articles are available on-line via the journal's website with a subscription. The journal is incorporated as a 501(c)(3) organization. References

Mathematics journals Publications established in 1951 Mathematical Sciences Publishers academic journals {{math-journal-stub ...
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Mathematische Zeitschrift
''Mathematische Zeitschrift'' (German for ''Mathematical Journal'') is a mathematical journal for pure and applied mathematics published by Springer Verlag. It was founded in 1918 and edited by Leon Lichtenstein together with Konrad Knopp, Erhard Schmidt, and Issai Schur. Past editors include Erich Kamke, Friedrich Karl Schmidt, Rolf Nevanlinna, Helmut Wielandt, and Olivier Debarre Olivier Debarre (born 1959) is a French mathematician who specializes in complex algebraic geometry.Debarr ...