(a) List all the generators of < 5 > in Z60. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60.
(a) List all the generators of < 5 > in Z6o. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60.
2. Suppose that < a> is a cyclic group of order 10. Find all the generators in terms of a)
5. Suppose H and K are subgroups of G and H 10, and |K-21. Prove that 6. Consider the subgroup <3 > of Z12. Find all the cosets of < 3>. How many distinct cosets are there?
List all the left cosets of H in G. a. and b. and H =< (123) > G= 44 H =< (1234) > G= 54
Let →a=2→i−5→j−2→ka→=2i→-5j→-2k→ and →b=5→i−→kb→=5i→-k→. Find −→a+→b-a→+b→. Let ā = 27 – 53 – 2k and 7 = 57 - K. Find - ã+ 7. <3i Х 5j k X>
5. Find a method-of-moments estimator (MME) of θ based on a randorn sample Xi, ,Xn from each of the following distributions 040<1 (b) f(r:0)-(0 + 1)re-2,T > 1, θ > 0
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
(5) Use induction to show that Ig(n) <n for all n > 1.
2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if and only if n and k are relatively prime.