(i) There are two non-isomorphic groups of order 4: C4 and
C2xC2. Let C3 be a cyclic group of order 3. For each group G of
order 4, determine all possible homomorphisms f an element of
Hom(C3, Aut(G)).
(ii) For C3 and each G of order 4 as above, determine all
possible homomorphisms phi an element of Hom(G, Aut(C3)).
1. Prove that the Cantor set contains no intervals.
2. Prove: If x is an element of the Cantor set, then there is a
sequence Xn of elements from the Cantor set converging
to x.
Let G be a cyclic group generated by an element a.
a) Prove that if an = e for some n ∈ Z, then G is
finite.
b) Prove that if G is an infinite cyclic group then it contains
no nontrivial finite subgroups. (Hint: use part (a))
One hundred students were placed into two groups. The two groups
were the South Beach diet and Keto diet. Below are the data for
pounds lost after 1 month of dieting. Assume the data are normal
and that the sample size is 100 (but, use the values you have).
Tell me if there is a difference between the two diets. Show all of
your work.
SB
Keto
2.5
3.5
3.2
3.7
3.0
4.0
5
4.1
2.3
4.0
2.7
2.5
1.0...
How do I prove the following: Show that for comparing two
groups, the Kruskal-Wallis test is equivalent to the Mann-Whitney
test. Please explain the meaning of each test statistic and
identify the distribution each one follows.