.Let be a group of order 36 and let be a normal subgroup of order 6. Let be an element of period 4.
a) Explain why
Because the period of any element must divide the order of the gorup that the element is in. 4 | 36 so but 4 does not divide 6 so
b) What is the order of the factor group
order is 6 because order divides order = 6
c) Work out that is trivial in
, which is the trivial coset
d) Prove has period 2 in
Neither (why?) nor (why?These two claims are, in
fact, one and the same thing...), but still , thus...
e) Prove that
This follows at once from (c) and from
For some reason when it comes to doing periods of cosets I get confused. Can anyone help me out?
Thanks in advance,