Prove that any two groups with one element are isomorphic.
Prove that any two groups with two elements are isomorphic.
Prove that any two groups with three elements are
isomorphic.
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))
Let a be an element of a finite group G. The order of a is the
least power k such that ak = e.
Find the orders of following elements in S5
a. (1 2 3 )
b. (1 3 2 4)
c. (2 3) (1 4)
d. (1 2) (3 5 4)
Your assignment is to examine the identity and cultural
structure of a non-U.S. Cultural group in the following areas:
1. Give a brief history of the culture - this history should
include information that lead to major changes within the cultural
behaviors or the group.
2. Give a description of the culture's worldview - multiple
views may be present. Include values, belief and social
practices.
3. What is the primary language of the culture and how is it
used? Discuss...