Intereting Posts

Is there a solution to $a^4+(a+d)^4+(a+2d)^4+(a+3d)^4+\dots = z^4$?
Dimension of a vector space is even implies Ker T = Im T.
Find a branch of $f(z)= \log(z^3-2)$ that is analytic at $z=0$.
Equivalent condition for differentiability on partial derivatives
Integration and differentiation of Fourier series
Getting an X for Chinese Remainder Theorem (CRT)
The Space $C(\Omega,\mathbb{R})$ has a Predual?
$\frac{dx}{dt}=-\lambda x +\epsilon x(t-a)$ series solution via Laplace method
Are there unique solutions for $n=\sum_{j=1}^{g(k)} a_j^k$?
What is the difference between probability and statistics?
How to show that every Suslin tree is Frechet-Urysohn
Proof of the extreme value theorem without using subsequences
$\lim_{x\to c} f(x)=L$
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
A set that it is uncountable, has measure zero, and is not compact

Let $K$ be the group generated by four elements $x_1,\cdots,x_4$ with relations that each generator commutes with all its conjugates. (An equivalent relation is, any simple commutator with repeated generator is trivial; for example, $[[x_2,[x_1,x_3]],x_3]=1$.) It can be proved that $K$ is finitely presented.

Let $A$ be the subgroup of $K$ generated by the following elements:

- Classifying groups of order 12.
- Reconciling Different Definitions of Solvable Group
- Is every element of a finite group a product of elements of prime order?
- Passage to fixed point spaces is object function of a contravariant functor?
- Strict cyclic order
- Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.

- $x_1x_2x_3x_4$;
- $[x_1,x_2][x_1,x_3][x_1,x_4][x_2,x_3][x_2,x_4][x_3,x_4]$;
- $[x_1,x_2,x_3][x_1,x_2,x_4][x_1,x_3,x_4][x_2,x_3,x_4]$;
- $[x_1,x_3,x_2][x_1,x_4,x_2][x_1,x_4,x_3][x_2,x_4,x_3]$;
- $[x_1,x_2,x_3,x_4]$;
- $[x_1,x_2,x_4,x_3]$;
- $[x_1,x_3,x_2,x_4]$;
- $[x_1,x_3,x_4,x_2]$;
- $[x_1,x_4,x_2,x_3]$;
- $[x_1,x_4,x_3,x_2]$.

Now I would like to compute the abelianization of $A$; namely, the group $A/[A,A]$, where $[A,A]$ is the commutator subgroup of $A$. My question is:

**Is there any way that I can use GAP to find the abelianization of $A$?**

As I never used GAP before, I am not familiar with how to input my question into GAP. A note of my notation: in my question $[a,b]=aba^{-1}b^{-1}$ and $[a,b,c,d]$ means $[[[a,b],c],d]$. If it is hopeless to apply GAP to my problem, is there any way that I can attack my problem by hand?

- Could this identity have an application?
- Group Theory - Proving $(a*b)^{-1} = (a^{-1}) * (b^{-1}) $
- Infinite Groups with Finitely many Conjugacy Classes
- Solving Rubik's cube and other permutation puzzles
- No group of order 36 is simple
- $p\mid $ then $p\mid $
- Infinite group must have infinite subgroups.
- Relation between semidirect products, extensions, and split extensions.

- The probability of having $k$ successes before $r$ failures in a sequence of independent Bernoulli trials
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- How to solve for any given natural number n?
- 'Proof' of the correspondence between maximal ideals and points in projective space
- Find the sum of $\sum_{n=1}^\infty (-1)^{n+1} x^{2n-1}$
- How to solve this Complex inequality system
- Proving : Every infinite subset of countable set is countable
- Integrability of Maximal Convolution Operator
- How does an odd order group affect the kernel?
- Vandermonde-like identities
- Is there an easy way to calculate $\displaystyle\lim_{k \to \infty} \frac{(k+1)^5(2^k+3^k)}{k^5(2^{k+1} + 3^{k+1})}$?
- The homomorphism defined by the system of genus characters
- If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
- Proof of Angle in a Semi-Circle is of $90$ degrees
- What does “removing a point” have to do with homeomorphisms?