Difference between revisions of "Join of abelian subgroups of maximum order"

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(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...)
 
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==Definition==
 
==Definition==
  

Revision as of 22:43, 26 January 2009

Template:Prime-parametrized subgroup-defining function

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 termed the Thompson subgroup, is defined as the subgroup of P generated by all abelian subgroups of maximum order in P.

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.