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Proof or Disprove 'If every proper subgroup of G is cyclic then G must be cyclic'?
Wiki User
∙ 12y ago
No! Take the quaternion group Q_8.
Wiki User
∙ 12y ago
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Proof of Clausius inequality for reversible process?
Clausius Inequality is not only for reversible process Since overall (system + surrounding) entropy always increase. (∆s) system + surrounding ≥ 0 For a cyclic process (∆s) system = 0 So (∆s) surrounding ≥ 0 Note that in cyclic integral of (dQ/T) dQ is positive for heat entering system form surrounding. So for surrounding change in entropy after a cyclic process is given by cyclic integral of (-dQ/T) which is ≥ 0 Thus cyclic integral of (dQ/T) ≤ 0
Why is a hypothesis important to a scientist?
Once a hypothesis have been confirmed through numerous experimental tests, it can then become a theory. Theories are much more powerful and expansive in scope than hypotheses. Once a theory has been established, it is the role of scientist to try and disprove a theory rather than to try to reinforce its proof.
How do you prove that a group of order 3 is cyclic?
Any group must have an identity element e. As it has order 3, it must have two other elements, a and b. Now, clearly, ab = e, for if ab = b, then a = e:abb-1 = bb-1, so ae = e, or a = e.This contradicts the givens, so ab != b. Similarly, ab != a, leaving only possibility: ab = e. Multiplying by a-1, b = a-1. So our group has three elements: e, a, a-1.What is a2? It cannot be a, because that would imply a = e, a contradiction of the givens. Nor can it be e, because then a = a-1, and these were shown to be distinct. One possibility remains: a2 = a-1.That means that a3 = e, and the powers of a are: a0 = e, a, a2 = a-1, a3 = e, a4 = a, etc. Thus, the cyclic group generated by a is given by: = {e, a, a-1}.QED.Let g be any element other than the identity. Consider , the subgroup generated by g. By Lagrange's Theorem, the order of is either 1 or 3. Which is it? contains at least two distinct elements (e and a). Therefore it has 3 elements, and so is the whole group. In other words, g generates the group.QEDIn fact here is the proof that any group of order p where p is a prime number is cyclic. It follow precisely from the proof given for order 3.Let p be any prime number and let the order of a group G be p. We denote this as|G|=p. We know G has more than one element, so let g be an element of the group and g is not the identity element in G. We also know contains more than one element and ||1 such that gn =1 if such an n exists.
A second type of proof in geometry is a proof by or indirect proof?
contradiction
Second type of proof in geometry is a proof by?
I am not really sure what you are asking but there are 3 types of proofs in geometry a flow proof, a 2-collumn proof, and a paragraph proof.
What is the definition of the word evidence?
evidence : that which tends to prove or disprove something; ground forbelief; proof.
Where can you find the video of the proof of God's existence?
There is no proof of God existing, though there is also no proof that he doesn't. It's all a matter of belief, until we can prove or disprove God's existence.
What are the normal subgroups of general linear group?
The special linear group, SL(n,R), is a normal subgroup of the general linear subgroup GL(n,R). Proof: SL(n,R) is the kernel of the determinant function, which is a group homomorphism. The kernel of a group homomorphism is always a normal subgroup.
How do you fix an helicopter cyclic control?
You have a certified professional fix it.Ask to see proof they are certified and do not take their word for it.
What do you do if you are falsely accused of battery?
Attempt to disprove the allegation against you. If the accusers (or law enforcement's) proof is greater than your defense, you will be charged or convicted.
What is the difference between evidence and testimony?
Evidence refers to any material or information that can be used to prove or disprove a fact in a legal case, such as documents, physical objects, or witness statements. Testimony specifically refers to oral statements given by witnesses under oath during a legal proceeding. Testimony is a type of evidence that is based on what witnesses personally observed or experienced.
What in science disproves god?
Nothing in science disproves god. However, it is not up to "non-believers" to disprove god. It is the role of the creations to first provide proof of god. The burden of proof lies with the prosecution, extraordinary claims require extraordinary proof, etc etc.
Is it possible to prove a hypothesis by conducting rigorously controlled experiments?
Not technically, you can disprove it. And you can narrow the probability of the null hypothesis but proof by experimentation alone is not possible.
What is the burden of proof in a misdemeanor case?
In a misdemeanor case, the burden of proof is typically "beyond a reasonable doubt." This means that the prosecution must prove that the defendant is guilty of the crime charged to a high degree of certainty.
Proof of Clausius inequality for reversible process?
Clausius Inequality is not only for reversible process Since overall (system + surrounding) entropy always increase. (∆s) system + surrounding ≥ 0 For a cyclic process (∆s) system = 0 So (∆s) surrounding ≥ 0 Note that in cyclic integral of (dQ/T) dQ is positive for heat entering system form surrounding. So for surrounding change in entropy after a cyclic process is given by cyclic integral of (-dQ/T) which is ≥ 0 Thus cyclic integral of (dQ/T) ≤ 0
How would you Proof that benzene has a cyclic structure?
The catalytic hydrogenation of benzene gives the C6H12 which obeys the formula of Alkenes but do not react with Br2 and KMnO4 solution so it is a cyclic molecule cyclohexane, the formation of cyclohexane proves that benzene also exists in cyclic structure.
Did burden of proof on the issue of causation rests on the prosecution?
No. The prosecution only has to prove that you COMMITTED the offense. The issue of WHY (the cause) you did it is not a prosecutorial responsibility.
