You had better tell us what you want the expressions "union of two subgroups"Originally Posted by ThePerfectHacker
and "intersection of two subgroups" to mean. As it is they don't mean
anything as union and intersection are usually defined on sets. And a
groups is not a set, a set may be involved but the group is not the set,
and as rgep points out the naive union/intersection of the associated sets
of a pair of subgroups is not usually the set associated with another subgroup.