# 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 ...
• 37.5k
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....
• 17.6k
Accepted

### How to find all subgroups of a group in GAP

One should think in terms of conjugacy classes of subgroups: ...
• 6,952
Accepted

### How to check in GAP whether two groups are isomorphic

There are two aspects here: how to search such information in GAP, and how to actually check the isomorphism of two groups. First, the OP was quite close to guessing the name of the function, since ...
• 6,952
Accepted

### Is $\mathrm{gnu}(2304)$ known?

There are indeed $112\,184+1\,953+15\,641 993 = 15\,756\,130$ groups of order 2304, computed using an algorithm developed by Bettina Eick and myself. As Alexander Konovalov already kindly pointed out, ...
• 1,812
Accepted

### Proof that the Rubik’s Cube group is 2-generated

To start, we will use the example from "Analyzing Rubik's Cube with GAP". It creates the group generated by the six generators, corresponding to the six faces of the cube: ...
• 6,952
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 ...
• 6,952
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/...
• 6,572
Accepted

### Non-isomorphic groups with identical structure-description

StructureDescription will -- despite what was claimed in older implementations -- not identify groups up to isomorphism, but just indicate a decomposition. For ...
• 17.6k

• 6,565

### 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 ...
• 17.6k
Accepted

### Rubik's Revenge Cube in GAP

It depends on the definition of the puzzle: If the faces are colored uniformly, for example a swap of 5 and 6 is not seen in the puzzle. You can see this discrepancy in the group. We construct the ...
• 17.6k

### How many groups of order $2058$ are there?

I believe the answer is 91. This is calculated by looking at where the construction process hangs (conjugacy test of small cyclic subgroups with many regular orbits) and reducing this test for ...
• 17.6k