Question

every group of order $105$ has a cyclic normal subgroup of index $3$ ?

score 921 · Answer 1 · 2014-11-20 08:18:38

921

Views

every group of order $105$ has a cyclic normal subgroup of index $3$ ?

Published on 20 Nov 2014 - 8:18

score 595 · Answer 2 · 2014-11-20 15:49:00

595

Views

Equality of cosets implies equality of the original sets

Published on 20 Nov 2014 - 15:49

score 56 · Answer 3 · 2014-11-23 17:54:31

56

Views

The converse of Factor Group criterion

Published on 23 Nov 2014 - 17:54

score 340 · Answer 4 · 2014-11-23 18:30:54

340

Views

Testing Normality in a Group

Published on 23 Nov 2014 - 18:30

score 65 · Answer 5 · 2014-11-23 19:52:07

65

Views

Suppose $G$ is a group, with a subgroup $K$ and a normal subgroup $H$.

Published on 23 Nov 2014 - 19:52

score 70 · Answer 6 · 2014-11-25 01:02:55

70

Views

A Question on the Quotient Group and/or set of cosets

Published on 25 Nov 2014 - 1:02

score 122 · Answer 7 · 2014-11-25 05:32:35

122

Views

How to prove a subgroup is normal?

Published on 25 Nov 2014 - 5:32

score 150 · Answer 8 · 2014-11-25 16:03:39

150

Views

Normal Subgroups in Group Theory

Published on 25 Nov 2014 - 16:03

score 628 · Answer 9 · 2014-12-04 15:45:50

628

Views

Let $G$ be a group. If $H\leq G$ is a subgroup and $N\vartriangleleft G$, then $HN$ is a subgroup of $G$.

Published on 04 Dec 2014 - 15:45

score 1.7k · Answer 10 · 2014-12-06 11:34:52

1.7k

Views

Prove that H is a normal subgroup if and only if, $\forall a , b \in G, ab \in$ H implies $ba\in H.$

Published on 06 Dec 2014 - 11:34

score 150 · Answer 11 · 2014-12-11 08:00:31

150

Views

A group in between the commutator subgroup and the original group must be normal

Published on 11 Dec 2014 - 8:00

score 910 · Answer 12 · 2026-03-26 11:03:16

910

Views

let $G$ be dihedral group so that $D_{2n}= \langle x,y \ | \ x^2=y^n=e, yx=xy^{n-1} \rangle$. Prove that $N\unlhd G$ and $G/N \cong W = \{1,-1\}$

Published on 26 Mar 2026 - 11:03

score 169 · Answer 13 · 2014-12-12 17:22:34

169

Views

Cosets of a Normal Subgroup, Quotient Group

Published on 12 Dec 2014 - 17:22

score 86 · Answer 14 · 2014-12-12 18:47:09

86

Views

show that there exist an element $g$ of a group $G$ such that $g^q$ is in $H$

Published on 12 Dec 2014 - 18:47

score 59 · Answer 15 · 2014-12-13 06:52:48

59

Views

If $N \lhd G, (G : N) = 100, a \in G, a^{23} = e$, show that $a \in N$.

Published on 13 Dec 2014 - 6:52

List Question

every group of order $105$ has a cyclic normal subgroup of index $3$ ?

Equality of cosets implies equality of the original sets

The converse of Factor Group criterion

Testing Normality in a Group

Suppose $G$ is a group, with a subgroup $K$ and a normal subgroup $H$.

A Question on the Quotient Group and/or set of cosets

How to prove a subgroup is normal?

Normal Subgroups in Group Theory

Let $G$ be a group. If $H\leq G$ is a subgroup and $N\vartriangleleft G$, then $HN$ is a subgroup of $G$.

Prove that H is a normal subgroup if and only if, $\forall a , b \in G, ab \in$ H implies $ba\in H.$

A group in between the commutator subgroup and the original group must be normal

let $G$ be dihedral group so that $D_{2n}= \langle x,y \ | \ x^2=y^n=e, yx=xy^{n-1} \rangle$. Prove that $N\unlhd G$ and $G/N \cong W = \{1,-1\}$

Cosets of a Normal Subgroup, Quotient Group

show that there exist an element $g$ of a group $G$ such that $g^q$ is in $H$

If $N \lhd G, (G : N) = 100, a \in G, a^{23} = e$, show that $a \in N$.

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