Question

Use Langrange's Theorem to see if you can conclude that a proper subgroup H of G is cyclic

score 28 · Answer 1 · 2019-04-03 23:28:45

28

Views

Use Langrange's Theorem to see if you can conclude that a proper subgroup H of G is cyclic

Published on 03 Apr 2019 - 23:28

score 296 · Answer 2 · 2019-04-04 20:41:57

296

Views

$K$-rational points on an elliptic curve

Published on 04 Apr 2019 - 20:41

score 128 · Answer 3 · 2019-04-06 10:50:34

128

Views

There is an element with order $p$

Published on 06 Apr 2019 - 10:50

score 4.2k · Answer 4 · 2019-04-09 15:46:11

4.2k

Views

Find the number of generators of a cyclic group with a given order n

Published on 09 Apr 2019 - 15:46

score 522 · Answer 5 · 2026-03-25 12:31:58

522

Views

Prove that a permutation is a $p$-cycle

Published on 25 Mar 2026 - 12:31

score 550 · Answer 6 · 2019-04-10 19:18:29

550

Views

Finding the left cosets for cyclic group $G=\langle a\rangle>$ of order $12$ and the cyclic subgroup $H=\langle a^4\rangle$

Published on 10 Apr 2019 - 19:18

score 807 · Answer 7 · 2026-03-26 22:18:14

807

Views

Let $G= \langle a \rangle$ be a cyclic group and $H$ a subgroup of $G$. Show $(G/H,*)$ is a cyclic group with generator $aH$.

Published on 26 Mar 2026 - 22:18

score 62 · Answer 8 · 2026-03-25 09:28:34

62

Views

Does there exist an infinite non-abelian group, such that all its nontrivial proper subgroups are isomorphic to $C_\infty$?

Published on 25 Mar 2026 - 9:28

score 947 · Answer 9 · 2026-03-27 16:19:16

947

Views

Generators for $\mathbb{Z_n}$

Published on 27 Mar 2026 - 16:19

score 757 · Answer 10 · 2026-03-25 09:25:38

757

Views

Group as direct sum of cyclic groups

Published on 25 Mar 2026 - 9:25

score 47 · Answer 11 · 2026-03-26 01:10:48

47

Views

Group of order $105$ with a normal Sylow $3$-subgroup is cyclic

Published on 26 Mar 2026 - 1:10

score 92 · Answer 12 · 2019-04-23 21:17:59

92

Views

Find the smallest $n \in \mathbb{N}$ such that the group is isomorphic to the direct product of $n$ cyclic groups

Published on 23 Apr 2019 - 21:17

score 70 · Answer 13 · 2026-03-26 14:29:31

70

Views

Graph $G$ with Degree $\ge 2$ must contain a cycle

Published on 26 Mar 2026 - 14:29

score 104 · Answer 14 · 2019-04-26 13:06:03

104

Views

How can an Infinity Group have the identity element e if e=e²=e³=...?

Published on 26 Apr 2019 - 13:06

score 121 · Answer 15 · 2019-04-27 18:13:01

121

Views

if $|G|=2n$ and for each divisor of $n$, set $\{g \in G ; g^{2k}=e \}$ has at most $2k$ elements show that $G$ is cyclic.

Published on 27 Apr 2019 - 18:13

List Question

Use Langrange's Theorem to see if you can conclude that a proper subgroup H of G is cyclic

$K$-rational points on an elliptic curve

There is an element with order $p$

Find the number of generators of a cyclic group with a given order n

Prove that a permutation is a $p$-cycle

Finding the left cosets for cyclic group $G=\langle a\rangle>$ of order $12$ and the cyclic subgroup $H=\langle a^4\rangle$

Let $G= \langle a \rangle$ be a cyclic group and $H$ a subgroup of $G$. Show $(G/H,*)$ is a cyclic group with generator $aH$.

Does there exist an infinite non-abelian group, such that all its nontrivial proper subgroups are isomorphic to $C_\infty$?

Generators for $\mathbb{Z_n}$

Group as direct sum of cyclic groups

Group of order $105$ with a normal Sylow $3$-subgroup is cyclic

Find the smallest $n \in \mathbb{N}$ such that the group is isomorphic to the direct product of $n$ cyclic groups

Graph $G$ with Degree $\ge 2$ must contain a cycle

How can an Infinity Group have the identity element e if e=e²=e³=...?

if $|G|=2n$ and for each divisor of $n$, set $\{g \in G ; g^{2k}=e \}$ has at most $2k$ elements show that $G$ is cyclic.

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