Question

What is a subset of pentagon D_{5} that is a subgroup?
Why?, then give an example of a cyclic subgroup of pentagon
D_{5}

Answer #1

Give an example of each object described below, or explain why
no such object exists:
1. A group with 11 elements that is not cyclic.
2. A nontrivial group homomorphism f : D8 −→ GL2(R).
3. A group and a subgroup that is not normal.
4. A finite integral domain that is not a field.
5. A subgroup of S4 that has six elements.

Give an example where X is not Hausdorff, and A is a compact
subset of X, but A is not closed. Justify your claims with
proof.

Let F be a field. It is a general fact that a finite subgroup G
of (F^*,X) of the multiplicative group of a field must be cyclic.
Give a proof by example in the case when |G| = 100.

Give an example of a ternary cyclic code of length 8
and dimension 5.
Explain why the example is valid.

Give an counter example or explain why those are false
a) every linearly independent subset of a vector space V is a basis
for V
b) If S is a finite set of vectors of a vector space V and v
⊄span{S}, then S U{v} is linearly independent
c) Given two sets of vectors S1 and S2, if span(S1) =Span(S2), then
S1=S2
d) Every linearly dependent set contains the zero vector

Give an example of a nontrivial subgroup of a multiplicative
group R× = {x ∈ R|x ̸= 0}
(1) of finite order
(2) of infinite order
Can R× contain an element of order 7?

What is a positive externality? Give an example of one.
Explain why your example is an externality. How does society (via
government action) deal with positive externalities?

What are the factors of production and why are they important.
Give an example of each. Please use bullet points to make it easier
for me to understand your responses.

What makes a good tool for analyzing and interpreting data? And
why? Give an example.

Explain quantitive easing also give an example of why this is a
good policy then give an example of why this could be a bad
policy

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