Let G be a group and H a subgroup of G.(adsbygoogle = window.adsbygoogle || []).push({});

The book claims HH=H because H is a subgroup.

Group multiplication is defined as AB={(a,b): a in A, b in B}

So HH should be ordered pairs with each pair containing two identical elements in H. But why is the answer H, which is not an ordered pair?

I think they have used this definition http://en.wikipedia.org/wiki/Product_of_subgroups instead of http://en.wikipedia.org/wiki/Direct_product_(group_theory)

Are the two completely different? The latter they direct product. If one write HH does it not refer to direct product? I always thought not putting a sign such as X means the same thing as putting X. Or is this convention only for elements of a group. So when doing operations on whole groups, putting or not putting a sign has different consequences?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why HH=H?

**Physics Forums | Science Articles, Homework Help, Discussion**