Baumann subgroup corresponding to join of elementary abelian subgroups of maximum order

Baumann subgroup corresponding to one of the Thompson subgroups
Let $$p$$ be a prime number and $$P$$ be a finite p-group. The Baumann subgroup of $$P$$, denoted $$B(P)$$, is defined as the defining ingredient::centralizer in $$P$$ of the defining ingredient::first omega subgroup of the defining ingredient::ZJe-subgroup of $$P$$. In symbols:

$$\! B(P) := C_P(\Omega_1(Z(J_e(P))))$$

The ZJe-subgroup refers to the center of the defining ingredient::join of elementary abelian subgroups of maximum order.

Related functions

 * Baumann subgroup corresponding to join of abelian subgroups of maximum order
 * Oliver subgroup