Just getting into group theory, so don't be surprised if this doesn't make any sense. Also, since I'm a novice, I'm assuming this kind of group has already been named, although I can't find an example in any of my books or on Google. Does anyone recognize this? I'd like to study it further..(adsbygoogle = window.adsbygoogle || []).push({});

Let <a> = A and <b> = B be two cyclic groups with |a| = n and |b| = m. Since <a> is a subgroup of S_n and <b> is a subgroup of S_m then there must be some larger group for S_{n+m} so that both <a> and <b> are subgroups. So then define the subgroup of S_{n+m} which are all possible products of a and b.

I guess another way to describe it would be the minimal union of two disjoint groups <a>, <b>.

Any ideas?

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# What kind of group is this?

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