Baumann subgroup corresponding to join of abelian subgroups of maximum order

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This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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Definition

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 centralizer in P of the first omega subgroup of the ZJ-subgroup of P. In symbols:

\! B(P) := C_P(\Omega_1(Z(J(P))))

Here, the ZJ-subgroup refers to the center of the join of abelian subgroups of maximum order.

Relation with other subgroup-defining functions

See also Baumann subgroup corresponding to join of elementary abelian subgroups of maximum order.