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Puig Subgroup
In mathematical finite group theory, the Puig subgroup, introduced by , is a characteristic subgroup of a ''p''-group analogous to the Thompson subgroup In mathematical finite group theory, the Thompson subgroup J(P) of a finite ''p''-group ''P'' refers to one of several characteristic subgroups of ''P''. originally defined J(P) to be the subgroup generated by the abelian subgroups of ''P'' of m .... Definition If ''H'' is a subgroup of a group ''G'', then ''L''''G''(''H'') is the subgroup of ''G'' generated by the abelian subgroups normalized by ''H''. The subgroups ''L''''n'' of ''G'' are defined recursively by *''L''0 is the trivial subgroup *''L''''n''+1 = ''L''''G''(''L''''n'') They have the property that *''L''0 ⊆ ''L''2 ⊆ ''L''4... ⊆ ...''L''5 ⊆ ''L''3 ⊆ ''L''1 The Puig subgroup ''L''(''G'') is the intersection of the subgroups ''L''''n'' for ''n'' odd, and the subgroup ''L''*(''G'') is the union of the subgroups ''L''''n'' for ''n'' even. Properties Puig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thompson Subgroup
In mathematical finite group theory, the Thompson subgroup J(P) of a finite ''p''-group ''P'' refers to one of several characteristic subgroups of ''P''. originally defined J(P) to be the subgroup generated by the abelian subgroups of ''P'' of maximal rank. More often the Thompson subgroup J(P) is defined to be the subgroup generated by the abelian subgroups of ''P'' of maximal order or the subgroup generated by the elementary abelian subgroups of ''P'' of maximal rank. In general these three subgroups can be different, though they are all called the Thompson subgroup and denoted by J(P). See also *Glauberman normal p-complement theorem *ZJ theorem *Puig subgroup, a subgroup analogous to the Thompson subgroup References * * *{{Citation , last1=Thompson , first1=John G. , author1-link=John G. Thompson , title=A replacement theorem for p-groups and a conjecture , doi=10.1016/0021-8693(69)90068-4 , mr=0245683 , year=1969 , journal=Journal of Algebra ''Journal of Algeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
