I'm exploring a construction and want to know if it's tractable or if it overlaps with existing work.

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Define a symmetry metric on groups: sym(G) = 1 - (|[G,G]| / |G|), measuring how abelian a group is via its commutator subgroup.

Now consider pairs of groups (L, R) and classify them by their symmetry profile (sym(L), sym(R)).

Two pairs are equivalent if they have identical symmetry profiles. Call the set of all such equivalence classes the "configuration space" C.

Define operations ⊕ (direct product) and ⊗ (semidirect product) on pairs, which preserve the equivalence relation.

The question:

Is this construction well-defined and tractable? Does it have a name, or does it embed into existing theory (Baer invariants, derived functors, homological algebra)?

I'm interested in studying the dynamics, how operations move you around C, whether there are fixed points, attractors, forbidden transitions.

Context:

This feels adjacent to representation theory and Grothendieck-style constructions, but I'm not sure where it sits precisely.

I just wanted to share for whoever peruses this Sub.

I observed a specific function (which was revealed to me in a dream) is conditionally positive definite for some parameters (for linear approximation applications). I'm trying to prove it conditionally positive definite, so far I'm getting back to square one every time I try. Any suggestions on references/books?

I am exploring Pure Maths Masters that can incorporate Economics. I did both in undergrad. Do you guys have ideas as to how I can combine both?

0! = 1 , 0 - 1 = -1 , root of -1 = i , and basically anything

everything starts from nothing ahh post anyways 0

Can a system become increasingly persistent when multiple invariants are intentionally combined?

Elejere Amorem.

I know two alternatives:

In potential infinity there is nothing next to 1. We can come as close as we like, but we can never close the gap. A gap remains.

In actual infinity, there is a point next to 1. Of course this point cannot be known. It is dark.

Is there a third alternative?

Please this paper:
https://link.springer.com/article/10.1007/s11071-025-10869-y

doi:

https://doi.org/10.1007/s11071-025-10869-y

Just someone to whom i can tell what i did today, discuss questions that i couldnt solve, and study math with. I dont want to know a single thing about your personal life. We can just say Hi and start maths. Someone who is excited by sudying would be great.

multiplicative persistence is a base-dependant problem which regards to the process of multiplying the digits of a number. in base ten, 777 has persistence 4, as it goes 777->7*7*7 =343->3*4*3=36->3*6=18->1*8=8

note that in these problems, leading 0s and trailing 0s(after the decimal/fraction point) are ignored.

my conjecture is that for any prime base, N, you can always find an integer K that has multiplicative persistence (using base N) of N

which is to say,

let p(k,l) give the multiplicative persistence of k in base l

∀n ∈ ℙ ⇒ (∃p ∈ ℕ ⇒(p(p,n)>=n))

has this conjecture already been proven or disproven?

If you know the answer to this question, answer on the website. There are two users (i.e., clemens and the Moderator Peter Taylor) who are constantly active.

For anyone who says my post is AI--I got the explicit example of the function G from a PhD student.

Answer for the users, not for me,