# All Questions

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### combine 4* 4 bytes values into 4 bytes and extract each value separately using one byte keys.

Here's my problem , I have 4 * 4 bytes i.e a,b,c,d and each one is 4 bytes length I want to generate x = function(a,b,c,d) , where x is 4 bytes and generate aKey,bKey,cKey,dKey where each key is 1 ...
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### commutator (derived) subgroup of S3

how can i calculate it easily? i showed that the commutator group of S3 is generated by (123) in S3 using the fact that S3 is isomorphic to D6 and relation in D6 but that was tedious...are there any ...
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### subgroups of the free product of a finite cyclic group and an infinite cyclic group.

How can I find all the subgroups of the free product $G = \mathbb{Z}*\mathbb{Z_2}$? I tried to answer this by looking at the subgroups of $\mathbb{Z}$ and $\mathbb{Z_2}$ separately. The subgroups of ...
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### Positive definite quadratic form . Riemannian manifolds

Does anybody know how to solve it? I've done a lot of tries but I didn't succeeded Let $H^n=\{ (x_0,x_1,...,x_n)\in \Re^{n+1}:x_0^2+x_1^2+...+x_n^2=-1,x_0>0\}$ and the symetric bilinear form ...
Let be $T:\mathbb{R}^7\rightarrow \mathbb{R}^7$ Such that $(T-15I)^3=0$ and $\dim\text{Im}(T-15I)^2=2$ find the Jordan normal form of $T$ If $(T-15I)^3=0$ so the minimal polynomial can be ...