Recent content by catcherintherye

I was wondering if anyone knows a more efficient method of finding conjugacy classes than the one i am currently using. tex/ Example D_6* =<x,y| x^3=1, y^4=1, yx=x^2y> now to find the conjugacy classes of this group i would first write out the orbit of x <x> ={ 1x1, xxx^2, x^2xx...

hello, I've been reading some proofs and in keep finding this same argument tyo prove that a linear map is injective viz, we suppose that t(a,c) = 0 and then we deduce that a,c = 0,0. is it the case that the only way a linear map could be non injective is if it took two elements to zero? i.e. t...

obviously i haven't made myself clear, i'll post the question in it's entirety... Let A,B be algebras over a field F. We say that A and B are isomorphic over F written A\cong_F B when there exists a bijective ring homomorphism \varphi : A \rightarrow B which is also linear over F, i.e...

I have about 5 questions all of a similar form ... \mathbb{F}[C_2] \cong \mathbb{F} \times \mahbb{F} if 1+1 \neq 0 in \mathbb{F} \Re [C_3] \cong \Re \times C \Re [C_4] \cong \Re \times \Re \times C these were on the first sheet given out and I still don't know how to do...

In the statement of Maschke's theroem we are told 'Let G be a finite group and F a field in which |G| not equal to zero. As an example we are told if our group was C2 (cyclic) then we could not have F=F2 (the field with 2 elements). I fail to see how C2 and F2 are related, surely |C2|=2...

i don't think so, the variables y_i, z_j are dual variables, i don't think they have units as such. The primal problem was to minimize cost subject to some constraints, more specifically, minimize \sum_{i=1}^{4}\sum_{j=1}^{6}c_ij x_ij subject to x_ij \geq 0 \sum_{j=1}^{6}x_ij \leq...

hello,I have been given the transportation problem (T) defined by the cost matrix \left(\begin{array}{ccccccc}5&3&9&3&8&2\\5&6&3&15&7&16\\9&20&10&22&17&25\\3&7&3&14&9&14\end{array}\right) the demand vector q=(2,8,9,4,6,2) the supply vector p=(3,13,6,9) the problem is as...

btw, i really need a prompt answer if at all possible, this is for my referal which has to be in next week!

hello,I have been given the transportation problem (T) defined by the cost matrix \left(\begin{array}{ccccccc}5&3&9&3&8&2\\5&6&3&15&7&16\\9&20&10&22&17&25\\3&7&3&14&9&14\end{array}\right) the demand vector q=(2,8,9,4,6,2) the supply vector p=(3,13,6,9) the problem is as...

i am working with the following linear program (P) max 2x_1 - x_2 subject to x_1 \leq 3 - x_1 + x_2 \leq -1 x_1 + x_2 \geq 2 x_1, x_2 \geq 0 my question is this, when introducing slack variable...

i am working with the following linear program (P) max 2x_1 - x_2 \\ subject to x_1 \leq 3 \\ - x_1 + x_2 \leq -1 \\ x_1 + x_2 \geq 2 \\ x_1, x_2 \geq 0 my question is this, when introducing slack variable...

okay so I'm going through the proof of sylow part 2, i.e. the bit that says if N_p is the number of subgroups of G of order p^n then N_p \equiv1modp now I have got to the part where I have taken the subgroup P of order P^n that you get from sylow part 1 and I have to show that it is a...

factorize x^{22} -3x^{11} + 2 right so I have p(x) = (x^11 -2)(x^11 - 1) (x^11 -2) satifies eisentstein, obviously x-1 is a factor of the second factor. Long division reaps x^{10} + x^9 +...+x + 1 the solution asserts that this is also irreducible, but I do not see this?? Is this...

show that there is a normal subgroup of G of order 5 when G is a group of order 30. My friend just called me with this problem, he said the usual method of solution fails. (i.e. using sylow and then showing that the subgroup is unique and deducing that it must therefore be normal), I told him to...

ta, the last bit was what I was looking for