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## Prove that two given groups are nonisomorphic

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.13 Prove that the following pairs of groups are not isomorphic: (1) $\mathbb{Z} \times Z_2$ and $\mathbb{Z}$,…

## Prove that a given group is not cyclic

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.12 Prove that the following groups are not cyclic: (1) $Z_2 \times Z_2$, (2) $Z_2 \times \mathbb{Z}$,…

## Exhibit the cyclic subgroups of Dih(8) as sets

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.11 Find all cyclic subgroups of $D_8$. Exhibit a proper subgroup of $D_8$ which is not cyclic.…