### Answers (7)

 3 All composition and Chief series for $S_n$ $n \geq 4$ 2 Factoring $x^5-1$ over $\mathbb{Z_5}$ 1 How to transform $\int_0^\infty x(1+x^2)^{-2}dx$ to $0,1$ as limits of the integral? 1 if $f$ is continuous then is $\sqrt f$continuous? 1 What will be the value of $ab$?

### Reputation (147)

 +15 If V is a vector space then (V,+) is a characteristically simple abelian group +10 Why does a one-to-one homomorphism from $G$ to $G/H\times G/K$ imply $G$ is solvable? +45 All composition and Chief series for $S_n$ $n \geq 4$ +10 How to transform $\int_0^\infty x(1+x^2)^{-2}dx$ to $0,1$ as limits of the integral?

### Questions (6)

 3 If V is a vector space then (V,+) is a characteristically simple abelian group 2 Why does a one-to-one homomorphism from $G$ to $G/H\times G/K$ imply $G$ is solvable? 1 Convergence of $b_n = \frac{\sum_{i=1}^na_i}{4}$ 0 G is [property] if and only if N and G/N are both [property] 0 Tangent spaces of two transverse subspaces are transverse subspaces

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 5 abstract-algebra × 3 1 integers 3 group-theory × 4 1 functions 2 number-theory 1 continuity 2 ring-theory 1 change-of-variable 1 real-analysis × 3 1 integration

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