Structure of $A_4/H$

Question

I was reading about $A_4$ and $S_4$ groups and I got curious about some of the subgroups. And if we have $H:= \{(),(12)(34),(13)(24),(14)(23)\}$, how would I determine and how would the structure look like of the quotient group $A_4/H$ and is $A_4$ a simple group?

No, $A_4$ is not simple since $H$ is a nontrivial normal subgroup. — Dietrich Burde, Jun 12 '20 at 16:53

score 0 · Answer 1 · answered Jun 12 '20 at 16:52

0

$H$ is normal and the corresponding factor group is cyclic of order three.

answered Jun 12 '20 at 16:52

Maryam

1,889

And how can I show that $H$ Is normal subgroup in that case? – variableXYZ Jun 12 '20 at 17:41
For example by computing its three cosets and noticing that right cosets and left ones coincide. – Maryam Jun 12 '20 at 17:42

Structure of $A_4/H$

1 Answers1