Andreas Caranti
Reputation
40,569
82/100 score
 Apr 29 comment Are Z and Z* (defined below) isomorphic as rings? Apr 27 comment Solving a Word Problem relating to factorisation Please use $\LaTeX$ to format your questions/answers. Also, people here on MSE appreciate seeing what you have tried. Apr 26 revised Formal product of cycles in a permutation group added 132 characters in body Apr 26 revised Formal product of cycles in a permutation group edited body Apr 26 answered Formal product of cycles in a permutation group Apr 26 revised $\bigcup_{n=1}^{\infty}G_n$ is a multiplicative subgroup of the group $\mathbb C\setminus\{0\}$ LaTeX editing Apr 25 comment Motivation for proving any nontrivial normal subgroup of $A_5$ has a 3-cycle? Just to add to @TobiasKildetoft comment, $a^b = a [a, b]$. Apr 24 answered Question about normal subgroups and conjugacy Apr 24 answered Image and Kernel of composition of two homomorphisms Apr 24 comment Showing $\mathbb{Q} \times \mathbb{Q}$ is not a field You should have seen that in a field, a product is zero iff one of the factors is zero. Because if $a b = 0$, and $b \ne 0$, you can multiply by $b^{-1}$ to get $a = 0$. Apr 24 answered Showing $\mathbb{Q} \times \mathbb{Q}$ is not a field Apr 24 comment Nomenclature for linear transformation Most likely the symbol is "$\mid$", and as noted it means "restricted to". Please try and use $\LaTeX$ to get the symbols right. Apr 23 comment Number of errors detected from a generator matrix There are two codewords $00000$ and $10100$ at distance $2$, so you can go from one to the other with two errors, and you won't notice. Apr 23 revised Number of errors detected from a generator matrix added 367 characters in body Apr 23 answered Number of errors detected from a generator matrix Apr 22 comment How do I get the Rational Canonical Form from the minimal and characteristic polynomials? Yes. The relevant Wikipedia article gives some more details. Apr 22 comment Direct sum and $FG$ homomorphism Look, $\pi$ acts like this. Take $z \in V$. You can write it uniquely as $z = z_{1} + \dots + z_{r}$, with $z_{i} \in U_{i}$. Now $\pi$ tales $z$ to $z_{i}$. Take $v = v_{1} + \dots + v_{r}$, with $v_{i} \in U_{i}$. Then $z = v g = v_{1} g + \dots v_{r} g$. Since $v_{i} g \in U_{i}$, we have $z_{i} = v_{i} g$. Now $\pi$ takes $z$ to $z_{i}$, that is, $v g$ to $v_{i} g$. Apr 22 answered How do I get the Rational Canonical Form from the minimal and characteristic polynomials? Apr 22 answered Why can I cancel in modular arithmetic when working modulus a prime number? Apr 22 answered Direct sum and $FG$ homomorphism