query: Is $Z^*_5$ a group of order 4 under modular multiplication? What type is it then(isomorphic to which one)
positive_passages.docid: 150204
positive_passages.text: Isomorphisms between the groups $U(10), U(5)$ and $\mathbb{Z}/4\mathbb{Z}$
negative_passages.docid: 8694
negative_passages.text: $A_4$ is not isomorphic to $D_6$
negative_passages.docid: 102429
negative_passages.text: There are 2 groups of order 6 (up to isomorphism)
negative_passages.docid: 40321
negative_passages.text: $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
negative_passages.docid: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 147574
negative_passages.text: Prove of a finite cyclic group of order $n$ is isomorphic tto $(\mathbb Z_n,+)$.
negative_passages.docid: 33025
negative_passages.text: What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
negative_passages.docid: 133612
negative_passages.text: How many isomorphisms are there from $\Bbb Z_{12}$ to $\Bbb Z_{4} \oplus \Bbb Z_{3}$?
negative_passages.docid: 21108
negative_passages.text: Perfect squares and modularly congruency in mod 5
negative_passages.docid: 23279
negative_passages.text: Group Theory Isomorphism
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 4648
negative_passages.text: Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
negative_passages.docid: 90437
negative_passages.text: Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
negative_passages.docid: 65968
negative_passages.text: Prove that any two cyclic groups of the same order are isomorphic?
negative_passages.docid: 22783
negative_passages.text: Is the set $Z_n = \{ 0, 1, . . . , n-1 \}$ for $n ≥ 1$ is a group under addition modulo n?