# Tag Info

Accepted

### How to solve this solvable 8th-degree algebraic equation by radicals?

Well, in honor of an old cartoon I'll say a miracle occurs. But can we get behind the curtain to see how the special effects are made? If you take the square root of, let us say, $2358$ by the ...
• 41.1k
Accepted

### How is GAP generating all subgroups?

GAP stores precomputed lists of subgroups of (automorphism groups) of a number of simple subgroups, the rest is computed on the fly. However it uses far more group theory than only considering subsets....
• 18.8k
Accepted

### Sylow $2$-subgroup Mathieu Group $M_{24}$

While I would emphasize Derek Holt's remark on that "identification" does not make much sense, here is a way that shows the Sylow subgroup to be isomorphic to the semidirect product of an ...
• 18.8k
Accepted

### List Conjugacy Classes in GAP?

Let's create some group as an example: gap> G:=Group((1,9,6,7,5)(2,10,3,8,4), (1,10,7,8)(2,9,4,6)); Group([ (1,9,6,7,5)(2,10,3,8,4), (1,10,7,8)(2,9,4,6) ]) It ...
• 7,022
Accepted

### Groups of derangements: what is known about subgroups of a symmetric group $S_{n}$ that contain only derangements (plus the identity)?

Such a group is sometimes called semiregular (or free, or fixed point free, although the later two are more often reserved for group actions than permutation groups), see https://en.wikipedia.org/wiki/...
• 6,769

• 6,205

### How do i see how all the generators get mapped during automorphism in GAP

The notation ^perm denotes an inner automorphism -- conjugation by the indicated permutation. The result tells you that $S_3$ has no outer automorphisms. If you ...
• 18.8k

### In GAP, How can I check whether a given group is a direct product?

The question would be more interesting if you asked how you might do this rather than asking whether there is a command to do it in GAP. Here is a first suggestion, which you could easily implements ...
• 92.1k
Accepted

### Monster coefficients

In GAP, you could simply iterate in a triple loop over $\phi,\psi,\rho$, calculate the $g$-values and find maximum and sum values: ...
• 18.8k

### Can graphs in GAP be obtained as a visual output

A standard tool for visualizing graphs is the graphviz software. The following GAP program ...
• 18.8k

### Subgroups of $\operatorname{GL}_2(\mathbb Z/8\mathbb Z)$

GAP is open source. You can download and install it as explained here. Then, for example, you can do the following. Create the group in question: ...
• 7,022

### If I kill any element $g$ of a group $G$ and as a result $G/\langle\langle g\rangle\rangle$ is killed, is $G$ then cyclic?

The answer is no. For example, if $G$ is any non-abelian simple group, then $G/\langle\langle g\rangle\rangle$ is trivial for every $g \neq e$, but $G$ is not abelian.
• 133k
Accepted

### how to save a file in GAP

LogTo(filename) will just print everything that you see in your terminal to a file (including output and errors), so you won't be able to read it in. If you want to store your input to read in later, ...
• 488
Accepted

### Computing endomorphism ring of finite groups via computer

In GAP, AllHomomorphismClasses is (and I'm writing this as the person who wrote the function) a "toy" function that is provided to try small examples in ...
• 18.8k