# Join of abelian subgroups of maximum order

From Groupprops

Revision as of 21:32, 26 January 2009 by Vipul (talk | contribs) (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...)

## Definition

Let be a group of prime power order. The **join of Abelian subgroups of maximum order** in , sometimes denoted and also termed the **Thompson subgroup**, is defined as the subgroup of generated by all abelian subgroups of maximum order in .

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.