About: Focal subgroup theorem

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In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application of the transfer" according to . The focal subgroup theorem relates the ideas of transfer and fusion such as described in. Various applications of these ideas include local criteria for p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p.

Attributes	Values
rdf:type	yago:WikicatTheoremsInGroupTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Focal subgroup theorem (en)
rdfs:comment	In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application of the transfer" according to . The focal subgroup theorem relates the ideas of transfer and fusion such as described in. Various applications of these ideas include local criteria for p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p. (en)
dcterms:subject	Theorems in group theory P-groups
Wikipage page ID	25971038 (xsd:integer)
Wikipage revision ID	1019229934 (xsd:integer)
Link from a Wikipage to another Wikipage	Derived subgroup Algebraic topology Index of a subgroup Inventiones Mathematicae Normal subgroup Simple group Generalized quaternion group Equivariant cohomology Hall subgroup Journal of Algebra Theorems in group theory American Mathematical Society Alperin–Brauer–Gorenstein theorem P-core Abelian group Abstract algebra Kernel (group theory) Sylow subgroup P-groups Homotopy theory Modular representation theory Reflective subcategory Dihedral group Dover Publications Philip Hall Order (group theory) Canadian Journal of Mathematics Category theory Upper p-series Finite group P-group Transactions of the American Mathematical Society Split exact sequence Springer-Verlag P-nilpotent group Finite index Quasi-dihedral group Nilpotent residual
Link from a Wikipage to an external page	http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002173409 https://www.ams.org/online_bks/surv402
sameAs	Focal subgroup theorem Focal subgroup theorem Focal subgroup theorem Focal subgroup theorem
suggestion	Control of transfer leads to various p-nilpotence results; include Tate and Thompsons hyperfocal O^p and "hypo" focal E^p results; include the character theoretic transfer and the work of Yoshida; contrast to control of fusion of elements and to control of strong fusion (en)
dbp:wikiPageUsesTemplate	dbt:! dbt:Anchor dbt:Citation dbt:Expand_section dbt:Harv dbt:Main
date	January 2010 (en)
has abstract	In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application of the transfer" according to . The focal subgroup theorem relates the ideas of transfer and fusion such as described in. Various applications of these ideas include local criteria for p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p. (en)
prov:wasDerivedFrom	wikipedia-en:Focal_subgroup_theorem?oldid=1019229934&ns=0
page length (characters) of wiki page	15957 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Focal_subgroup_theorem
is Link from a Wikipage to another Wikipage of	Index of a subgroup Lower p-series Focal subgroup Sylow theorems Transfer (group theory) Reflective subcategory List of theorems P-group P-residual subgroup
is Wikipage redirect of	Lower p-series Focal subgroup P-residual subgroup
is foaf:primaryTopic of	wikipedia-en:Focal_subgroup_theorem

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