Question

Why is $a^k$ → $k$ mod $n$ one-to-one?

score 50 · Answer 1 · 2017-10-26 18:18:56

50

Views

Why is $a^k$ → $k$ mod $n$ one-to-one?

Published on 26 Oct 2017 - 18:18

score 721 · Answer 2 · 2026-03-28 09:50:16

721

Views

Determining order of elements and number of automorphisms in dihedral groups

Published on 28 Mar 2026 - 9:50

score 301 · Answer 3 · 2017-10-27 15:35:22

301

Views

Show that $\left(\Bbb{C}^*,\cdot\right)$ is not cyclic

Published on 27 Oct 2017 - 15:35

score 694 · Answer 4 · 2017-10-28 14:42:26

694

Views

If $G$ is cyclic with order $N$ then $g^n$ has order $\frac{N}{\gcd(n,N)}$

Published on 28 Oct 2017 - 14:42

score 783 · Answer 5 · 2017-10-28 16:54:55

783

Views

Prove that the given group is not cyclic

Published on 28 Oct 2017 - 16:54

score 94 · Answer 6 · 2017-10-29 16:34:24

94

Views

Group theory (cyclic groups)

Published on 29 Oct 2017 - 16:34

score 160 · Answer 7 · 2017-10-30 01:57:33

160

Views

Group of order $2^n m$ ($m$ odd) with a cyclic Sylow $2$-subgroup has a characteristic subgroup of order $m$.

Published on 30 Oct 2017 - 1:57

score 1.9k · Answer 8 · 2017-10-31 22:33:37

1.9k

Views

Is a non cyclic group isomorphic to a cyclic group?

Published on 31 Oct 2017 - 22:33

score 1.1k · Answer 9 · 2017-11-04 21:25:57

1.1k

Views

Finding all the generators of $Z_{n}$

Published on 04 Nov 2017 - 21:25

score 2.5k · Answer 10 · 2017-11-04 21:49:35

2.5k

Views

How to say that any group of order $pqr$ is cyclic with a provided relation between $p$, $q$, $r$, where they are all distinct primes.

Published on 04 Nov 2017 - 21:49

score 129 · Answer 11 · 2017-11-07 13:49:24

129

Views

What is the Wedderburn decomposition of $\mathbb{F}_p[C_n]$?

Published on 07 Nov 2017 - 13:49

score 166 · Answer 12 · 2017-11-07 18:22:54

166

Views

Order of largest cyclic subgroup of $A_4 \times S_5$?

Published on 07 Nov 2017 - 18:22

score 1.2k · Answer 13 · 2017-11-10 02:49:28

1.2k

Views

Abstract Algebra: U(n) groups and cyclic groups

Published on 10 Nov 2017 - 2:49

score 393 · Answer 14 · 2017-11-13 14:22:03

393

Views

If we have $mr + ns = 1$, how do we prove that $\operatorname{GCD}(m,n) = 1$?

Published on 13 Nov 2017 - 14:22

score 89 · Answer 15 · 2017-11-13 19:14:09

89

Views

Proof of $(ab)^n=a^nb^n$ is fulfilled when it is true for $n = 2$

Published on 13 Nov 2017 - 19:14

List Question

Why is $a^k$ → $k$ mod $n$ one-to-one?

Determining order of elements and number of automorphisms in dihedral groups

Show that $\left(\Bbb{C}^*,\cdot\right)$ is not cyclic

If $G$ is cyclic with order $N$ then $g^n$ has order $\frac{N}{\gcd(n,N)}$

Prove that the given group is not cyclic

Group theory (cyclic groups)

Group of order $2^n m$ ($m$ odd) with a cyclic Sylow $2$-subgroup has a characteristic subgroup of order $m$.

Is a non cyclic group isomorphic to a cyclic group?

Finding all the generators of $Z_{n}$

How to say that any group of order $pqr$ is cyclic with a provided relation between $p$, $q$, $r$, where they are all distinct primes.

What is the Wedderburn decomposition of $\mathbb{F}_p[C_n]$?

Order of largest cyclic subgroup of $A_4 \times S_5$?

Abstract Algebra: U(n) groups and cyclic groups

If we have $mr + ns = 1$, how do we prove that $\operatorname{GCD}(m,n) = 1$?

Proof of $(ab)^n=a^nb^n$ is fulfilled when it is true for $n = 2$

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