Let G be a cyclic group of order 20 generated by an element a, and let H be a subgroup of G generated by the element a^4. List all the cosets of H in G. It is known that H is normal. Give the operation table for the quotient group G/H.
Awms A
Favorite Answer
H = {e, a^4, a^8, a^12, a^16}
aH = {a, a^5, a^9, a^13, a^17}
a^2 H = {a^2, a^6, a^10, a^14, a^18}
a^3 H = {a^3, a^7, a^11, a^15, a^19}
There's no good way to give the operation table for G/H in this textbox. Needless to say, it looks like a cyclic group of order 4, generated by aH, where, for example,
(aH)(aH) = a^2 H
and
(aH)(a^3 H) = a^4 H = H.