Question

find all subgroups and normal subgroups of group Z2 x Z2 x Z2

Answer 1

any guesses?

Answer 2

for one thing, you only have to find the subgroups, since
\(\mathbb{Z_2^3}\) is abelian, and all subgroups must be normal

Answer 3

so up to isomorphism the the subgroups will be
\[\mathbb{Z_2\times Z_2}\] and
\[\mathbb{Z_2}\] plus i guess the trivial ones , the group itself and zero

Answer 4

i know if the group is abelian, and all subgroups are normal..
But from this link http://mathworld.wolfram.com/FiniteGroup.html , there are 16 number subgroups of group Z2 x Z2 x Z2 , but it is written only 4 number of normal. Is this true or not?

Answer 5

i think since it is abelian, so all subgroups are normal.. Thank you..:)