Intereting Posts

Tricky Lebesgue Dominated Convergence Question
A Banach space is reflexive if a closed subspace and its quotient space are both reflexive
Codifferential of a $p$-vector in components
What is $iav-\log(v)$? Any series expansion or inequality for it?
A question of H.G. Wells' mathematics
Second part of the factorial sum divisibility question
Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$
Efficient computation of $\sum_{k=1}^n \lfloor \frac{n}{k}\rfloor$
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
Determining the number $N$
Sum of sets of measure zero
Find the center of the symmetry group $S_n$.
Prove that the intersection of a finite number of open sets is open.
Number of zeros at the end of $k!$
Adjoint Functor Theorem

Possible Duplicate:

A Nontrivial Subgroup of a Solvable Group

If $H$ is nontrivial normal subgroup of the solvable group $G$, then how can I show that there is a nontrivial subgroup $A\leq H$ such that $A$ is abelian and normal in $G$?

I am looking for hints so that I can create my own solution.

- Cardinality of the quotient ring $\mathbb{Z}/(x^2-3,2x+4)$
- Find all subrings of $\mathbb{Z}^2$
- Applications of Abstract Algebra to elementary mathematics
- How to show this presentation of the additive group $(\mathbb{Q},+)$?
- Neutral element in $\hom_C(A, B)$
- If $b$ is algebraic over a finite extension $K$ of $F$ then $\mid $

Thank you all.

- “The Egg:” Bizarre behavior of the roots of a family of polynomials.
- Prove the direct product of nonzero complex numbers under multiplication.
- How to factor ideals in a quadratic number field?
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- Conjugacy classes of $\mathcal D_{10}$.
- Intersection of prime ideals
- Let $G$ be a group of order 35. Show that $G \cong Z_{35}$
- Finding a nonempty subset that is not a subgroup

Hints (for you to prove):

1) It is true that

$$H\geq H’\geq\ldots\geq H^{(n)}=1\,\, ,\,\, \text{for some}\,\,\,n\in\Bbb N$$

2) Show that $\,H^{(n-1)}\triangleleft G\,\;\;$ (Yes, not only in $\,H\,$ …!)

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- Have arrows in a category with this property a special name?
- Infinite expected value of a random variable
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- List of functions not integrable in elementary terms
- Homogeneous topological spaces
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- solving third-order nonlinear ordinary differential equation
- How do I prove that $X^{p^n}-X$ is the product of all monic irreducible polynomials of degree dividing $n$?