Powering-invariant subgroup of Lazard Lie group is Lazard Lie group
Statement
Suppose is a Lazard Lie group and is a powering-invariant subgroup of . Then, is a Lazard Lie group itself, and hence, is a Lazard Lie subgroup of .
Suppose is a Lazard Lie group and
is a powering-invariant subgroup of
. Then,
is a Lazard Lie group itself, and hence, is a Lazard Lie subgroup of
.