Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $H = \{(1),(12)(34)\}$ and $\alpha_1 = (243), \alpha_2 = (142), \alpha_3 = (132),$ and $\alpha_4 = (234)$.

Coset multiplication is a bit confusing to me. The book states in an example that $\alpha_1H = \alpha_2H$ and I'd like to see it for myself, however not a single paragraph in this book actually explains the operation of $\alpha_1H$. As to why I wrote the other $\alpha_i$'s, the book claims that:

$\alpha_1 \alpha_3H \neq \alpha_2 \alpha_4H$

I just would like to see it for myself before I press forward.


share|cite|improve this question
up vote 2 down vote accepted

$\alpha_1 H$ just means you take every element in $H$ and multiply on the left by $\alpha_1$. So $$\alpha_1 H = \{\alpha_1 (1), \alpha_1 (12)(34)\} = \{(243)(1), (243)(12)(34)\} = \{(243), (142)\}$$ Can you compute $\alpha_2 H$ yourself? What about $\alpha_1\alpha_3 H$ and $\alpha_2 \alpha_4 H$?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.