# abstract algebra

1. ### Homomorphism

I know the formula that I have to show is true. However, I am confused where to start to prove it. I thought multiplying the 2 matrices together but that’s not possible. Can someone start me off please?
2. ### arithmetics

Hello, I am a student in discrete mathematics and I have trouble solving this problem. Any help track is welcome! Here is the problem: A boat sinks in the ocean and the 5 survivors each jump in a different lifeboat. They meet on the deserted island in the distance. The next morning, the first...
3. ### Sylow subgroup of some factor group.

Hi. Let $G$ be a finite group. Let $K$ be a subgroup of $G$ and let $N$ be a normal subgroup of $G$. Let $P$ be a Sylow $p$-subgroup of $K$. Is $PN/N$ is a Sylow $p$-subgroup of $KN/N$? Here is what I think. Since $PN/N \cong P/(P \cap N)$, then $PN/N$ is a $p$-subgroup of $KN/N$...
4. ### Show that groups are isomorphic

How to show that the group (Z_4, +4) is isomorphic to (<i>, .)?
5. ### semigroup research

hi guys! does anyone know where I can get resources on combinatorial algebraic properties of full transformation contraction mapping semigroups very urgent anyone who has an idea of what contraction mapping semigroup is about please let me know
6. ### Maximum allowable probability of error for the (8, 4) Hamming Code

What is the maximum allowable probability of error is a typical digit in order that the (8, 4) Hamming Code can be used with probability .999 that the receiver will not be misled (i.e., 3 or more errors occur) in a single word?
7. ### Karatsuba method

For polynomials f(x),g(x) of degree d = 2^(r-1)-1, how do I check that multiplying f(x) and g(x) by the Karatsuba method requires 3^(r-1) multiplications in the field F?

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