Abstract:
While MacLane's version of the Kurosh subgroup theorem for free products has
been well-known, one of its implications seems to have escaped the attention of
the mathematical community.
The purpose of this note is to fill this gap by
providing this implication.
It asserts that a nontrivial normal subgroup of a
group is a free factor of this subgroup's normal closure in the free product of
the group with arbitrary nontrivial groups.
Keywords:free product of groups, normal closure of a subgroup, the subgroup theorem for
free products.
