1
$\begingroup$

$U_8=1,3,5,7$ since this group has one element of order one, three elements of two order and no element of $4$ order .. so does the Klein group.

Both $U(8)$ and the Klein group are non cyclic groups whose every proper subgroup is cyclic, so the Klein group is isomorphic to U(8)?

$\endgroup$
1
$\begingroup$

There is only two groups of order four: (1) the cyclic group and (2) the Klein group.

As all elements of $U(8)$ are of order $2$, $U(8)$ is indeed isomorphic as a group to the Klein group.

The key argument is that there is no other groups of order four than the two mentioned above

$\endgroup$
  • $\begingroup$ hey can u help finding all proper subgroups of Z2 × Z2 × Z2 ? i want to know how to approach to such problems ..any methodol $\endgroup$ – Henry Dec 26 '18 at 13:27
  • $\begingroup$ I suggest you post another question to avoid mixing different topics. $\endgroup$ – mathcounterexamples.net Dec 26 '18 at 13:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.