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Tagged with congruences lattice-theory
2 questions
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Reference request for a proof of the fact that every congruence-permutable variety is semidegenerate
Given an algebra $\mathbf{A}$, a pair of congruences
$ \alpha ,\beta \in Con(\mathbf {A})$ are said to permute when
$ \alpha \circ \beta =\beta \circ \alpha$, and an algebra
$\mathbf{A}$ is called ...
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22
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Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?
If there is no restriction on $n$, this is a famous open problem. I'm wondering if any recent work has been done for small $n>6$. I believe the question is answered (positively) for $n=6$ by ...
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