Question

Find a primitive root of (a) $U(\mathbb{Z}/121\mathbb{Z})$, and (b) $U(\mathbb{Z}/18\mathbb{Z})$

score 138 · Answer 1 · 2026-05-05 06:20:47

138

Views

Find a primitive root of (a) $U(\mathbb{Z}/121\mathbb{Z})$, and (b) $U(\mathbb{Z}/18\mathbb{Z})$

Published on 05 May 2026 - 6:20

score 45 · Answer 2 · 2026-04-13 18:21:20

45

Views

Is the order of $ab^{-1}$ larger than $m$?

Published on 13 Apr 2026 - 18:21

score 291 · Answer 3 · 2026-04-10 02:53:37

291

Views

are permutation coordinate of a point linear independent under cyclic group with odd length?

Published on 10 Apr 2026 - 2:53

score 1.2k · Answer 4 · 2026-04-16 03:41:01

1.2k

Views

Prove that if $G$ is a cyclic group of order $n$, then $G$ is isomorphic to $\mathbb{Z}_{n}$.

Published on 16 Apr 2026 - 3:41

score 150 · Answer 5 · 2026-04-29 12:51:36

150

Views

Direct product of two finite monogenic semigroup

Published on 29 Apr 2026 - 12:51

score 690 · Answer 6 · 2026-04-13 22:09:00

690

Views

If group $G$ is cyclic, then quotient group $G/H$ is cyclic.

Published on 13 Apr 2026 - 22:09

score 261 · Answer 7 · 2026-04-16 17:36:09

261

Views

Trouble with a proof that all subgroups of a cyclic group are cyclic

Published on 16 Apr 2026 - 17:36

score 1.4k · Answer 8 · 2026-04-16 08:37:52

1.4k

Views

Find the order of $\sqrt{3}\in \mathbb{R}$ and $\sqrt{3}\in \mathbb{R}^{*}$.

Published on 16 Apr 2026 - 8:37

score 557 · Answer 9 · 2026-05-04 01:40:36

557

Views

Direct sum of cyclic groups of integers modulo.

Published on 04 May 2026 - 1:40

score 105 · Answer 10 · 2026-04-15 19:46:42

105

Views

If $|g|=15$ and $|h|=16$, find $|\left \langle g \right \rangle \cap \left \langle h \right \rangle|$.

Published on 15 Apr 2026 - 19:46

score 805 · Answer 11 · 2026-04-15 09:41:53

805

Views

Let p be prime. If a group has more than $p-1$ elements of order $p$, why can't the group be cyclic?

Published on 15 Apr 2026 - 9:41

score 125 · Answer 12 · 2026-04-15 19:58:17

125

Views

Prove that if $\phi: G\to H$ is a homomorphism and $G_{1}\leq G$ is cyclic, then $\phi (G_{1})$ is cyclic.

Published on 15 Apr 2026 - 19:58

score 42 · Answer 13 · 2026-04-15 03:58:24

42

Views

On the Sylow 2-subgroup of a finite group

Published on 15 Apr 2026 - 3:58

score 60 · Answer 14 · 2026-04-17 11:15:08

60

Views

Group of order $545$ is cyclic?

Published on 17 Apr 2026 - 11:15

score 127 · Answer 15 · 2026-04-17 02:46:14

127

Views

Prove that the only automorphism of order 2 of $\mathbb{Z}_q$ is $m \mapsto -m$ for $q = 3$ and $q = 5$ and $q = 7$

Published on 17 Apr 2026 - 2:46

List Question

Find a primitive root of (a) $U(\mathbb{Z}/121\mathbb{Z})$, and (b) $U(\mathbb{Z}/18\mathbb{Z})$

Is the order of $ab^{-1}$ larger than $m$?

are permutation coordinate of a point linear independent under cyclic group with odd length?

Prove that if $G$ is a cyclic group of order $n$, then $G$ is isomorphic to $\mathbb{Z}_{n}$.

Direct product of two finite monogenic semigroup

If group $G$ is cyclic, then quotient group $G/H$ is cyclic.

Trouble with a proof that all subgroups of a cyclic group are cyclic

Find the order of $\sqrt{3}\in \mathbb{R}$ and $\sqrt{3}\in \mathbb{R}^{*}$.

Direct sum of cyclic groups of integers modulo.

If $|g|=15$ and $|h|=16$, find $|\left \langle g \right \rangle \cap \left \langle h \right \rangle|$.

Let p be prime. If a group has more than $p-1$ elements of order $p$, why can't the group be cyclic?

Prove that if $\phi: G\to H$ is a homomorphism and $G_{1}\leq G$ is cyclic, then $\phi (G_{1})$ is cyclic.

On the Sylow 2-subgroup of a finite group

Group of order $545$ is cyclic?

Prove that the only automorphism of order 2 of $\mathbb{Z}_q$ is $m \mapsto -m$ for $q = 3$ and $q = 5$ and $q = 7$

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