Question

A group $(G,\circ)$ does not have any proper subgroups if and only if $\text{ord}(G)=p$,where $p$ is a prime number.

score 241 · Answer 1 · 2020-10-08 06:07:25

241

Views

A group $(G,\circ)$ does not have any proper subgroups if and only if $\text{ord}(G)=p$,where $p$ is a prime number.

Published on 08 Oct 2020 - 6:07

score 442 · Answer 2 · 2020-10-08 11:03:11

442

Views

Why "An infinite cyclic group is isomorphic to the set of integers" and not "there is bijection $\varphi: \mathbb Z \to \langle g \rangle$"

Published on 08 Oct 2020 - 11:03

score 527 · Answer 3 · 2020-10-08 23:04:32

Let $G$ be a cyclic group of order $15$. Suppose $x\in G$ and exactly two of $x^3,x^5$, and $x^9$ are equal. Find $|x^{12}|$ and $|x^{14}|$.

score 147 · Answer 4 · 2026-04-03 03:36:43

147

Views

Order of $\phi: g^i \mapsto g^{mi}$

Published on 03 Apr 2026 - 3:36

score 65 · Answer 5 · 2020-10-13 19:34:07

65

Views

Let $G$ a group and $a\in G$ such that $a$ is an element of finite order, then $\lvert \langle a \rangle\rvert=o(a)$.

Published on 13 Oct 2020 - 19:34

score 97 · Answer 6 · 2020-10-14 23:28:05

97

Views

Find a normalizer of order 3 in $S_7$ of cyclic subgroup in $S_7$

Published on 14 Oct 2020 - 23:28

score 1.2k · Answer 7 · 2020-10-15 13:17:53

1.2k

Views

Show that every proper subgroup of $S_3$ is cyclic.

Published on 15 Oct 2020 - 13:17

score 2k · Answer 8 · 2020-10-15 20:17:14

2k

Views

In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

Published on 15 Oct 2020 - 20:17

score 75 · Answer 9 · 2020-10-16 19:31:20

75

Views

A subgroup formed by elements of cyclic group raised to a power

Published on 16 Oct 2020 - 19:31

score 82 · Answer 10 · 2020-10-18 04:48:25

82

Views

The order of an element to the power of $k$ is less or equal to the order of an element

Published on 18 Oct 2020 - 4:48

score 682 · Answer 11 · 2020-10-20 11:40:00

682

Views

Every element of a finite group to the power of the order of the Group is 1 - is this true - what is the proof for this?

Published on 20 Oct 2020 - 11:40

score 189 · Answer 12 · 2020-10-21 10:43:42

189

Views

Finite Groups - order of the element divides order of the Group

Published on 21 Oct 2020 - 10:43

score 35 · Answer 13 · 2020-10-21 21:53:18

35

Views

Show the order of the Kernel of a morphism between groups

Published on 21 Oct 2020 - 21:53

score 37 · Answer 14 · 2020-10-22 00:47:15

37

Views

Show that exists a element with order $q-1$ in $\langle\overline{x}\rangle$

Published on 22 Oct 2020 - 0:47

score 120 · Answer 15 · 2020-10-22 21:38:58

120

Views

Describe all possible groups of order 102, up to isomorphism. Without using semidirect product.

Published on 22 Oct 2020 - 21:38

List Question

A group $(G,\circ)$ does not have any proper subgroups if and only if $\text{ord}(G)=p$,where $p$ is a prime number.

Why "An infinite cyclic group is isomorphic to the set of integers" and not "there is bijection $\varphi: \mathbb Z \to \langle g \rangle$"

Let $G$ be a cyclic group of order $15$. Suppose $x\in G$ and exactly two of $x^3,x^5$, and $x^9$ are equal. Find $|x^{12}|$ and $|x^{14}|$.

Order of $\phi: g^i \mapsto g^{mi}$

Let $G$ a group and $a\in G$ such that $a$ is an element of finite order, then $\lvert \langle a \rangle\rvert=o(a)$.

Find a normalizer of order 3 in $S_7$ of cyclic subgroup in $S_7$

Show that every proper subgroup of $S_3$ is cyclic.

In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

A subgroup formed by elements of cyclic group raised to a power

The order of an element to the power of $k$ is less or equal to the order of an element

Every element of a finite group to the power of the order of the Group is 1 - is this true - what is the proof for this?

Finite Groups - order of the element divides order of the Group

Show the order of the Kernel of a morphism between groups

Show that exists a element with order $q-1$ in $\langle\overline{x}\rangle$

Describe all possible groups of order 102, up to isomorphism. Without using semidirect product.

Trending Questions

Popular # Hahtags

Popular Questions