Join of abelian subgroups of maximum order - Revision history

Vipul at 20:15, 2 March 2009

2009-03-02T20:15:50Z

← Older revision		Revision as of 20:15, 2 March 2009
Line 3:		Line 3:
	==Definition==		==Definition==

	Let <math>P</math> be a [[group of prime power order]]. The '''join of Abelian subgroups of maximum order''' in <math>P</math>, sometimes denoted <math>J(P)</math> and also termed the '''Thompson subgroup''', is defined as the subgroup of <math>P</math> generated by all [[defining ingredient::abelian subgroup of maximum order\|abelian subgroups of maximum order]] in <math>P</math>.		Let <math>P</math> be a [[group of prime power order]]. The '''join of Abelian subgroups of maximum order''' in <math>P</math>, sometimes denoted <math>J(P)</math> and also termed the '''Thompson subgroup''' or the '''Thompson J-subgroup''', is defined as the subgroup of <math>P</math> generated by all [[defining ingredient::abelian subgroup of maximum order\|abelian subgroups of maximum order]] in <math>P</math>.

	Note that the term ''Thompson subgroup'' is also used for the [[join of abelian subgroups of maximum rank]] and for the [[join of elementary abelian subgroups of maximum order]].		Note that the term ''Thompson subgroup'' is also used for the [[join of abelian subgroups of maximum rank]] and for the [[join of elementary abelian subgroups of maximum order]].

			===As a characteristic p-functor===

			For a nontrivial <math>p</math>-group <math>P</math>, the subgroup <math>J(P)</math> is also nontrivial, since <math>P</math> has nontrivial abelian subgroups. Thus, this is a [[characteristic p-functor]], and in particular, is a [[conjugacy functor]]. A closely related, and extremely important, <math>p</math>-functor is the [[ZJ-functor]] whose many properties were explored by [[Glauberman]].

Vipul at 22:43, 26 January 2009

2009-01-26T22:43:03Z

← Older revision		Revision as of 22:43, 26 January 2009
Line 1:		Line 1:
			{{prime-parametrized subgroup-defining function}}

	==Definition==		==Definition==

Vipul: New page: ==Definition== Let $P$ be a group of prime power order. The '''join of Abelian subgroups of maximum order''' in $P$ , sometimes denoted $J(P)$ and also...

2009-01-26T21:32:20Z

New page: ==Definition== Let <math>P</math> be a group of prime power order. The '''join of Abelian subgroups of maximum order''' in <math>P</math>, sometimes denoted <math>J(P)</math> and also...

New page

==Definition==

Let <math>P</math> be a [[group of prime power order]]. The '''join of Abelian subgroups of maximum order''' in <math>P</math>, sometimes denoted <math>J(P)</math> and also termed the '''Thompson subgroup''', is defined as the subgroup of <math>P</math> generated by all [[defining ingredient::abelian subgroup of maximum order|abelian subgroups of maximum order]] in <math>P</math>.

Note that the term ''Thompson subgroup'' is also used for the [[join of abelian subgroups of maximum rank]] and for the [[join of elementary abelian subgroups of maximum order]].

Join of abelian subgroups of maximum order - Revision history

Vipul at 20:15, 2 March 2009

Vipul at 22:43, 26 January 2009

Vipul: New page: ==Definition== Let P be a group of prime power order. The '''join of Abelian subgroups of maximum order''' in P, sometimes denoted J(P) and also...

Vipul: New page: ==Definition== Let $P$ be a group of prime power order. The '''join of Abelian subgroups of maximum order''' in $P$ , sometimes denoted $J(P)$ and also...