Question

Order of element in multiplicative group modulo n, where n is not prime

score 2.6k · Answer 1 · 2026-02-23 13:44:39

2.6k

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Order of element in multiplicative group modulo n, where n is not prime

Published on 23 Feb 2026 - 13:44

score 674 · Answer 2 · 2026-03-28 00:06:18

674

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Why are the n-th roots of unity the only subgroup of order $n$ on $S^1$

Published on 28 Mar 2026 - 0:06

score 1.2k · Answer 3 · 2016-11-05 18:03:59

1.2k

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Prove that any finite cyclic group with more than two elements has at least two different generators

Published on 05 Nov 2016 - 18:03

score 340 · Answer 4 · 2026-03-28 16:17:29

340

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Abelian group of order $p^m$ having only one subgroup of order $p^{m-1}$

Published on 28 Mar 2026 - 16:17

score 1.2k · Answer 5 · 2016-11-09 18:15:47

1.2k

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Show that Z(7)\0 under modular multiplication is isomorphic to C(6)

Published on 09 Nov 2016 - 18:15

score 12.5k · Answer 6 · 2026-02-23 04:24:13

12.5k

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Let $A$ be an $n \times n$ matrix with real entries such that $A^2 + I = 0$ then $n$ is even.

Published on 23 Feb 2026 - 4:24

score 50 · Answer 7 · 2026-03-26 22:58:46

50

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Strategy for finding subgroups of the holomorph

Published on 26 Mar 2026 - 22:58

score 773 · Answer 8 · 2026-03-26 01:29:14

773

Views

Let G be a cyclic p-group with subgroups H and K. Prove that either H is contained in K or K is contained in H.

Published on 26 Mar 2026 - 1:29

score 84 · Answer 9 · 2026-03-28 10:40:38

84

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Number of decompositions

Published on 28 Mar 2026 - 10:40

score 3.2k · Answer 10 · 2026-03-29 12:52:51

3.2k

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Finding homomorphisms $f: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ with image of size $3$

Published on 29 Mar 2026 - 12:52

score 104 · Answer 11 · 2026-03-26 19:19:06

104

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$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

Published on 26 Mar 2026 - 19:19

score 7.3k · Answer 12 · 2016-11-15 12:51:02

7.3k

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Each finite cyclic group of order $n$ contains unique subgroup of order $d$ where $d\mid n$

Published on 15 Nov 2016 - 12:51

score 834 · Answer 13 · 2016-11-16 00:33:53

834

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G, a finite abelian and cyclic group, isomorphic to set of homomorphisms of G into C\{0}

Published on 16 Nov 2016 - 0:33

score 192 · Answer 14 · 2016-11-16 22:28:19

192

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Sum of elements of order $p$ in $(\mathbb{Z}/2p^2\mathbb{Z})^\times$?

Published on 16 Nov 2016 - 22:28

score 164 · Answer 15 · 2026-03-27 18:57:03

164

Views

The group $(\Bbb Z_{13}\setminus \{0\}, \cdot)$ is cyclic. Determine all its generators.

Published on 27 Mar 2026 - 18:57

List Question

Order of element in multiplicative group modulo n, where n is not prime

Why are the n-th roots of unity the only subgroup of order $n$ on $S^1$

Prove that any finite cyclic group with more than two elements has at least two different generators

Abelian group of order $p^m$ having only one subgroup of order $p^{m-1}$

Show that Z(7)\0 under modular multiplication is isomorphic to C(6)

Let $A$ be an $n \times n$ matrix with real entries such that $A^2 + I = 0$ then $n$ is even.

Strategy for finding subgroups of the holomorph

Let G be a cyclic p-group with subgroups H and K. Prove that either H is contained in K or K is contained in H.

Number of decompositions

Finding homomorphisms $f: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ with image of size $3$

$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

Each finite cyclic group of order $n$ contains unique subgroup of order $d$ where $d\mid n$

G, a finite abelian and cyclic group, isomorphic to set of homomorphisms of G into C\{0}

Sum of elements of order $p$ in $(\mathbb{Z}/2p^2\mathbb{Z})^\times$?

The group $(\Bbb Z_{13}\setminus \{0\}, \cdot)$ is cyclic. Determine all its generators.

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