so lets say |a| = 30. How many left cosets of <a^4> in <a> are there? ok, so |a| = 30. and think I need to find the order of <a^4> also. I thought the order of it is <a^4> = e, a^4, a^8, a^12, a^16, a^20, a^24, a^28. so it has order of 8. but my book said the order of it is 15.... is there a formula they used to figure this out?