Isomorphisms in finite abelian groups 1

Question

True of false? If G and H are two groups with the same order and both are abelian, then they are isomorphic.

score 4 · Answer 1 · answered Oct 30 '14 at 15:47

4

Am implication of this is that every finite abelian group is isomorphic to some cyclic group, which is not true.

answered Oct 30 '14 at 15:47

ncmathsadist

49,383

score 3 · Answer 2 · answered Oct 30 '14 at 15:48

3

$\textbf{HINT-}$ Consider $\mathbb{Z_4}$ and $\mathbb{Z_2 \times Z_2}$. So FALSE.

answered Oct 30 '14 at 15:48

Bhaskar Vashishth

11,279

score 0 · Answer 3 · answered Oct 30 '14 at 16:00

0

Any finite abelian group is isomorphic to direct product of prime power orders. So I can apply this for these two groups we get they are not isomorphic. Because if G is cyclic and H is not.

answered Oct 30 '14 at 16:00

Y2k walker

17

Isomorphisms in finite abelian groups 1

3 Answers3