Join of abelian subgroups of maximum order
From Groupprops
Template:Prime-parametrized subgroup-defining function
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.