Visual Group Theory, Lecture 3.4: Direct products

[@arisioz]

Are semidirect products covered in this series, if yes which lecture is it covered in?

[@alan2here]

The direct product of groups seems much akin to cartesian multiplication of graphs.

[@smackronme]

generators of exercise - a,b,c,ab,bc,ca,abc (these are cyclic) , ,,,,,, (non-cyclic) other two are identity and z2*z2*z2

[@dof3810]

Are solutions to the home work or exercises in Nathan's book on VGT available anywhere?

[@davidefanchini]

Are we sure there aren't 18 subgroups of Z2 * Z2 * Z2? Of course including the improper and trivial ones

[@scitwi9164]

16:40 Nooo! Don't burst my bubbles! T.T BTW is the direct product commutative or not?

[@antoniolewis1016]

No, it is not commutative.

[@hanyanglee9018]

Actually I believe it commutative. But I ignored the sequence of the elements. I mean, A direct multiple B is something (a,b)with some properties, and B x A is (b,a), but this sequence of lower a and b doesn't count imo. (a,b) as the result of A x B and (b,a) as result of B x A share the same set of properties. So I say the direct product commutative. They commutative in the aspect of property but not in the aspect of notation.

[@Mrpallekuling]

The direct product is commutative (and associative) up to isomorphism

[@smackronme]

1,1 example reminds me of emergent properties..