Questions tagged [classification]

Classification of various mathematical structures. For classification in the sense of statistics / machine learning, use [tag:statistical-classification].

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Characterization of Frobenius complements

I have learned that Frobenius complements are characterized (among finite groups) by having a fixed point free complex representation. That is, a finite group $G$ is a Frobenius complement if and only ...
Joonas Ilmavirta's user avatar
19 votes
4 answers
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Representation theorem for modular lattices?

Birkhoff's representation theorem implies that every distributive lattice embeds into the lattice of subsets of a set. Is there also some representation theorem for modular lattices? For example, I ...
Martin Brandenburg's user avatar
55 votes
2 answers
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How do you *state* the Classification of finite simple groups?

From the point of view of formal math, what would constitute an appropriate statement of the classification of finite simple groups? As I understand it, the classification enumerates 18 infinite ...
Mario Carneiro's user avatar
27 votes
1 answer
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Has anyone catalogued the "first generation" proof of the classification of finite simple groups?

It has been estimated that the original proof of the CFSG spans around 15,000 journal pages written by hundreds of authors over most of the 20th century. The GLS project attempted to simplify this ...
Mario Carneiro's user avatar
25 votes
2 answers
4k views

In what sense is the classification of all finite groups "impossible"?

I think there is a general belief that the classification of all finite groups is "impossible". I would like to know if this claim can be made more precise in any way. For instance, if there is a ...
Keivan Karai's user avatar
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13 votes
0 answers
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What are the known convex polyhedra with congruent faces?

Note: I originally asked this question on math.SE here, where I posted a bounty on the question but received no answers after a week despite apparent interest in the problem. I'm hoping MathOverflow ...
RavenclawPrefect's user avatar
12 votes
2 answers
2k views

basics of classification of trilinear forms (when is it non-discrete)

Consider tri-linear forms, $\{A_{ijk}\}$ where $i=1,..,n_1$, $j=1,..,n_2$, $k=1,..n_3$, over a field of zero characteristic, up to the equivalence $A\to (U_1,U_2,U_3)(A)$, by three matrices. What is ...
Dmitry Kerner's user avatar
9 votes
2 answers
467 views

The "Johnson polychora"

Firstly, a definition: A convex polyhedron, whose faces are regular polygons (2D polytopes). This includes the 92 Johnson solids, 13 Archimedean solids, 5 Platonic solids and two infinite ...
FusRoDah's user avatar
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5 votes
1 answer
473 views

Classification of the quotients of the ring Z/4 [X]

Is it possible to classify all cyclic $\mathbb{Z}/4$-algebras, i.e. the regular quotients of $\mathbb{Z}/4 [X]$? A typical example is $\mathbb{Z}/4 [X] / \langle X^n , 2 X^k \rangle$. For my purposes ...
Martin Brandenburg's user avatar
5 votes
0 answers
293 views

A class 3 group of order 243

Let G be a group of order $243=3^5$. We denote by $(G_i)$ its lower central series and assume that $G$ has class $3$ and that $|G:G_2|=|G_3|=9$. We assume moreover that the cubing map factors as a (...
user avatar
4 votes
1 answer
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Classification of finite abelian hypergroups and table algebras

Update: Originally, I formulated this question for finite abelian hypergroups, but in a discussion with Geoff Robinson below I realized that the abelian hypergroups defined below are equivalent to ...
Juan Bermejo Vega's user avatar
3 votes
1 answer
212 views

What is the growth of the rank of a power of a finite simple group?

Which asymptotic bounds (upper and lower) are known for $s_n$ - the minimal number of generators of $S^n$ where $S$ is a nonabelian finite simple group?
Pablo's user avatar
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