Make the Subgroup Lattices feature easier to find/more prominent

[kcrisman]

Perhaps include yet another column of info, Hasse diagram of subgroup lattice, and connect to the other stuff appropriately. Probably a big project, but could be another great addition. These do show up with some frequency in Visual Group Theory, anyway.

[nathancarter]

You can do this now. It's just a bit hard to find. Here's how:

• Click a group to open its group info window.
• Click to expand the Subgroups section.
• Find the text that reads, "The subgroups can also be shown arranged in a lattice, each shown as highlighted portions of the whole group, connected by the identity (inclusion) homomorphism. You may see that lattice by Cayley diagram, cycle graph, or multiplication table, ..."
• Each of those three visualizations is a link you can click to generate the lattice.

[kcrisman]

You were right that this was hard to find.

- Each of those three visualizations is a link you can click to generate the lattice.

Since this is a common thing to request, maybe it should have a bit more prominence on the first page? But also, I find that usually these are not as cool as your diagrams - they are just lists of elements, or sometimes of sets of generators. One could repurpose this ticket to add that format as a fourth option as well.

[nathancarter]

Yes, the prominence of this feature is a good point. I'm going to retitle this ticket to indicate as much.

But I'm not sure I understand what your final paragraph is saying. The subgroup lattices aren't as cool as the other kinds of visualizations? I would agree with that. But I'm not sure what you mean by saying they're just lists of generators, since they're a picture with a lot of diagrams in it...And when you're saying a fourth option, do you mean add it as another way to visualize the group, up under the Views section? (There are already four options there...?)

[kcrisman]

On Wed, Sep 9, 2020 at 10:17 AM Nathan Carter ***@***.***> wrote: Yes, the prominence of this feature is a good point. I'm going to retitle this ticket to indicate as much. But I'm not sure I understand what your final paragraph is saying. The subgroup lattices aren't as cool as the other kinds of visualizations? I would agree with that. But I'm not sure what you mean by saying they're just lists of generators, since they're a picture with a lot of diagrams in it...And when you're saying a fourth option, do you mean add it as another way to visualize the group, up under the Views section? (There are already four options there...?) No, what I mean is that the _typical_ subgroup lattice visualization isn't

as cool as yours! But they are still quite useful. So this ticket could be to make the lattices "advertised". But another one (obviously not high priority) would be having the "standard" lattice visualization as lists of elements/generators available as a fourth option. Like the one on various pages in your book that appear under Hasse diagrams in your index 😃

[nathancarter]

Ah, I see what you mean. Yes, GE doesn't currently do a diagram like that, because its only visualizers are actual pictures (mult table, cayley graph, etc.) rather than just some math notation listing generators. But it would be easy to add a visualization that's just a list of generators, to make such pictures. Let's break that out into a feature request. I'll start a new ticket for that separate from this one.

[nathancarter]

Issue added: #14

[rayellis4]

Would you suggest a label (list of generators) on the existing graphical visualization of the lattice too?

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On Wed, Sep 9, 2020 at 11:48 AM Nathan Carter ***@***.***> wrote: Issue added: #14 <#14> — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#11 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AKE4RFJLOJ3HGJKKJZAZNSDSE6WUBANCNFSM4Q77QT6A> .

[nathancarter]

Oh, maybe that's the better way to do it; just add labels under the existing visualizations. Then you get pictures and labels all in one.

[kcrisman]

Would you suggest a label (list of generators) on the existing graphical visualization of the lattice too?

Hmm, that is a good question. I'd make it an option (see below).

Oh, maybe that's the better way to do it; just add labels under the

existing visualizations. Then you get pictures and labels all in one. You could do that, but I think still having the "naked" labels is a useful one. Less distraction - visual group theory isn't _always_ the best way! Sometimes symbols are better, once in a while.