Originally Posted by

**Amer** when i said typo i mean in the book I made an example

let $\displaystyle G=Z_{24}$ , $\displaystyle H = <3> = \{0,3,6,9,...,21\}$ , $\displaystyle K = <4> = \{0,4,8,...,20\}$

$\displaystyle \mid H\mid = 8 , \mid K \mid = 6 $

H acting on xK by left additive

$\displaystyle G/K = \{K, 1+K,2+K,3+k\}$

the orbit of H acting on the left cost will be $\displaystyle \{K, 1+K,2+K,3+k\}$

$\displaystyle \mid HxK \mid = \mid K \mid . \mid H:Stab_H(xK)\mid = 6.4 = 24 $

but if it is $\displaystyle \mid HxK \mid = \mid H \mid . \mid H :Stab_H(xK) \mid = 8.4 = 32 ??$ which is not correct since the order should equal to the G order

so there is a typo in book

am I right ?