In finite group theory, a branch of mathematics, the Puig subgroup, introduced by , is a characteristic subgroup of a p-group analogous to the Thompson subgroup.
If H is a subgroup of a group G, then L<sub>G</sub>(H) is the subgroup of G generated by the abelian subgroups normalized by H.
The subgroups L<sub>n</sub> of G are defined recursively by
They have the property that
The Puig subgroup L(G) is the intersection of the subgroups L<sub>n</sub> for n odd, and the subgroup L<sub>*</sub>(G) is the union of the subgroups L<sub>n</sub> for n even.
Puig proved that if G is a (solvable) group of odd order, p is a prime, and S is a Sylow p-subgroup of G, and the '-core of G is trivial, then the center Z(L(S)) of the Puig subgroup of S is a normal subgroup of G.