Re: when is the union of two subgroups a subgroup?

On 04.09.2006 17:13, robert wrote:
"Jannick Asmus" <jannick.news@xxxxxx> wrote in message
news:44FC3539.5070003@xxxxxxxxx
On 04.09.2006 16:10, robert wrote:
Let H1,H2 be two subgroups of the group G.
When is H1UH2 a subgroup of G?
if H1 is contained in H2 or vice versa. Is the converse true, too?

I would say no. assume H1 be contained in H2 and let H1UH2 be a subgroup of
G. Then H2 is still a group since H2=H1UH2, but H1 is not necessarily a
subgroup of G since H1 is not required to contain the identity.

But H1 is a subgroup by assumption and, therefore, it does contain the
identity. In order to answer he question, show that if H1 is not
contained in H2 then H2 is contained in H1.
.

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