Question

$Gal(f)$ is cyclic of order $m$ for irreducible $f \in K[X]$ of degree $m$, where $K$ is a finite field

score 60 · Answer 1 · 2026-02-23 03:01:16

60

Views

$Gal(f)$ is cyclic of order $m$ for irreducible $f \in K[X]$ of degree $m$, where $K$ is a finite field

Published on 23 Feb 2026 - 3:01

score 850 · Answer 2 · 2026-03-25 16:13:58

850

Views

$G/H$ cyclic and $H$ subgroup of $Z(G)$, then $G$ cyclic.

Published on 25 Mar 2026 - 16:13

score 132 · Answer 3 · 2019-03-07 05:21:57

132

Views

Group theory problem - the order of elements

Published on 07 Mar 2019 - 5:21

score 93 · Answer 4 · 2019-03-07 12:17:06

93

Views

In a cyclic group with subgroup $H$ and $N$, list the elements in $H + N$ and $H \cap N$

Published on 07 Mar 2019 - 12:17

score 458 · Answer 5 · 2019-03-08 14:05:14

458

Views

What is the order of the element $10 \in (\mathbb Z/p \mathbb Z)^*$?

Published on 08 Mar 2019 - 14:05

score 509 · Answer 6 · 2019-03-11 19:13:32

509

Views

Let $G$ have exactly $24$ elements of order $6$. Why are there $12$ cyclic subgroups of $G$ of order $6$?

Published on 11 Mar 2019 - 19:13

score 693 · Answer 7 · 2019-03-12 18:45:18

693

Views

Are generators of finite cyclic groups unique?

Published on 12 Mar 2019 - 18:45

score 98 · Answer 8 · 2026-03-26 18:51:48

98

Views

prove that for $G$ a multiplicative nonabelian group of order $pq$, where $p$ and $q$ are prime numbers, any proper subgroup of $G$ is abelian

Published on 26 Mar 2026 - 18:51

score 73 · Answer 9 · 2026-03-26 21:27:36

73

Views

How to derive the relation between $k$ and $l$ given $\langle g^k \rangle = \langle g^l \rangle$ in a cyclic group $C_n = \langle g \rangle$?

Published on 26 Mar 2026 - 21:27

score 59 · Answer 10 · 2019-03-19 13:19:23

59

Views

Give three non-isomorphic groups of order 24, and explain why they are not isomorphic.

Published on 19 Mar 2019 - 13:19

score 352 · Answer 11 · 2019-03-28 00:29:13

352

Views

Galois Group of Q(6th roots of unity) over Q

Published on 28 Mar 2019 - 0:29

score 168 · Answer 12 · 2026-03-26 12:52:42

168

Views

Finding quadratic residues without Legendre symbols

Published on 26 Mar 2026 - 12:52

score 69 · Answer 13 · 2019-03-30 19:50:28

69

Views

Given a pair of primes $g < p$, is there an efficient test if $g$ is a generator of the group $\mathbb{Z}_p^*$?

Published on 30 Mar 2019 - 19:50

score 80 · Answer 14 · 2019-04-01 02:34:05

80

Views

Is 2 always a generator of the unit group Z_{3^m} for any nonzero positive integer m?

Published on 01 Apr 2019 - 2:34

score 74 · Answer 15 · 2026-03-25 17:44:04

74

Views

What is the factor group $C_{12}/C_{6}$?

Published on 25 Mar 2026 - 17:44

List Question

$Gal(f)$ is cyclic of order $m$ for irreducible $f \in K[X]$ of degree $m$, where $K$ is a finite field

$G/H$ cyclic and $H$ subgroup of $Z(G)$, then $G$ cyclic.

Group theory problem - the order of elements

In a cyclic group with subgroup $H$ and $N$, list the elements in $H + N$ and $H \cap N$

What is the order of the element $10 \in (\mathbb Z/p \mathbb Z)^*$?

Let $G$ have exactly $24$ elements of order $6$. Why are there $12$ cyclic subgroups of $G$ of order $6$?

Are generators of finite cyclic groups unique?

prove that for $G$ a multiplicative nonabelian group of order $pq$, where $p$ and $q$ are prime numbers, any proper subgroup of $G$ is abelian

How to derive the relation between $k$ and $l$ given $\langle g^k \rangle = \langle g^l \rangle$ in a cyclic group $C_n = \langle g \rangle$?

Give three non-isomorphic groups of order 24, and explain why they are not isomorphic.

Galois Group of Q(6th roots of unity) over Q

Finding quadratic residues without Legendre symbols

Given a pair of primes $g < p$, is there an efficient test if $g$ is a generator of the group $\mathbb{Z}_p^*$?

Is 2 always a generator of the unit group Z_{3^m} for any nonzero positive integer m?

What is the factor group $C_{12}/C_{6}$?

Trending Questions

Popular # Hahtags

Popular Questions