Factor groups question

**DCU** · Jan 25th 2011, 10:17 AM

Basically I know how to do the first part, it's just the multiplication table giving me problems. I know the headings for the table should be H, (1,2)H, (1,3)H, (2,3)H, (1,2,3)H, (1,3,2)H but I don't know anymore.

**Haven** · Jan 25th 2011, 03:03 PM

Multiplication in factor groups is easy. It is defined as
$(aH)(bH) = abH$ .

For example Let $G=\mathbb{Z}, H = Z\mathbb{Z}$ . Since G is abelian, H is normal in G.

Consider two cosets of $4\mathbb{Z}$ , $(1+ 4\mathbb{Z}) +(2+4\mathbb{Z}) = (3 + 4\mathbb{Z})$ .

Now in your example, we take $[(12)H][(24)H] = (14)H$ . since $(12)(24) = (14)$

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