Its not cyclic because no permutation can be a generator for the group. That is, no one permutation when composed with itself however many times can generate all the permutations within the group.
Is that correct?
Oh okay. I think I was just outleveling myself for a minute. The next part of the question ask if the subgroup of even permutations is cyclic. I guess what I have shown is the proof that it is cyclic.
Thanks for your help jbunniii
Homework Statement
Consider the group of permutation on the set {123}. Is this group cyclic? Justify your answer
Homework Equations
The Attempt at a Solution
I wrote out the cayley table for this group, and noticed that if we take (123)^3 = e . Seeing as we can get back to the...
Okay, So I subbed in x = r cos (alpha) and y = r sin (alpha) and simplified the expression down to
1 + 5r^3(cos(alpha))^2(sin(alpha))^3
My question is, because as the lim r-> 0 then isn't the limit just 1 (which is what I wanted to show) and I wouldn't have to use the squeeze theorem if...
Oh, sorry I did mean the third one. I copied and pasted directly from a pdf file and it messed up the formatting without me realising sorry. Ill try the polar coordinates now thx.
Hi,
I'm having a lot of difficulty with finding limits of multivariable functions. A question like this comes up every year in the final exam and it will always ask for use of the squeezing theorem.
Homework Statement
(a) Suppose that
f(x, y) = 1 +(5x2y3)/x2 + y2
for (x, y) =/=...
Homework Statement
Let a,b,c,d be elements of a group G and let ab = c, bc = d, cd = a, da = b. Examine the expression da^2b and first derive an expression for b in powers of a. Then express c and d in powers of a. Show that a^5 = e (identity element)
Homework Equations
The Attempt...
Hi,
By leaving everything to the last minute I managed to flunk all my math courses this year. As such I now have 4 resit exams in August to prepare for. The courses are
Introduction to Analysis
Sets and Algebraic structures
Linear Algebra
Advanced Calc (goes up to about Calc II level...
Homework Statement
Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation
(Ill write ddz/ddt for the partial derivative of z wrt t and
dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.)
ddz/ddt +...
Homework Statement
Let f: N -> N be a bijective map. for n Є N
a sub n = 1 / f(n)
Show that the sequence (a sub n) converges to zero.
Homework Equations
The Attempt at a Solution
Basically I have been stuck on this problem for hours now and have read through my notes and...
Homework Statement
Let X = {a,b,c,d}. How many different equivalence relations are there on X? What subset of
XxX corresponds to the relation whose equivalence classes are {a,c},{b,d}
Homework Equations
N/A
The Attempt at a Solution
So I wrote out all the possible "blocks"...