All Questions
Tagged with lattices finite-groups
9 questions
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Products of maximal inclusions of finite groups with a non-obvious intermediate
Let $(H_1 \subset G_1)$ and $(H_2 \subset G_2)$ be core-free maximal inclusions of finite groups.
Their product, the inclusion $(H_1 \times H_2 \subset G_1 \times G_2)$, admits four obvious ...
5
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Are the homogeneous single chain subfactors, Dedekind?
Background: See here and there.
Recall that a subfactor is Dedekind if all its intermediate subfactors are normal.
A subfactor $(N \subset M)$ is Homogeneous Single Chain (HSC) if its lattice ...
37
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2
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A group-theoretic perspective on Frankl's union closed problem
Here is a group theoretic phrasing of a special case of the union closed conjecture:
Question: Given a finite group $G$, is there an element of prime power order which is contained in at most half ...
- 85.6k
16
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Maximal number of maximal subgroups
Let $G$ be a finite group. I want to find an upper bound on the number of the maximal subgroups. My questions is does it possible to prove that the number of maximal subgroups of any finite group $G$ ...
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12
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24 vectors in Leech lattice having scalar product $\frac{1}{4}$ pairwise
Two vectors from Leech lattice - as defined on wikipedia - have scalar product $\pm 32,\pm 16, \pm 8$ or $0$. Do there exist 24 vectors having scalar product 8 pairwise ? When we consider unit vectors ...
user21230
7
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Are the distributive permutation groups linearly primitive?
An action of a group $G$ on a set $X \neq \emptyset$ is called transitive if $\forall x,y \in X$, $\exists g \in G$ such that $g.x = y$.
It is called primitive if it is transitive and preserves no non-...
3
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What's the ratio of inclusions of finite groups with a distributive lattice?
Definition: Two inclusions of finite groups are equivalent, $(A \subset B) \sim (C \subset D)$, if: $(A/A_B \subset B/A_B) \simeq (C/C_D \subset D/C_D)$ with $A_B$ the normal core of $A$ in $B$.
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1
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Existence of homogeneous single chain compositions of a given maximal subfactor?
All the subfactors here are irreducible inclusion of hyperfinite II$_1$ factors.
A subfactor $(N \subset M)$ is Homogeneous Single Chain ($HSC$) if its lattice of intermediate subfactors is a single ...
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1
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Map homemade Leech lattice to classic one
In following question on MathOverflow I received construction of new Leech lattice provided by Noam Elkies. Let's call it $(E)$. This Leech lattice has nice feature that there is easy to see $24$ ...
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