4 problems

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Wall's conjecture on maximal proper subgroups of finite groups
About 10 years old
For a finite group $G$ , let $\max(G)$ denote the number of maximal proper subgroups of $G$ . Wall's conjecture. … This conjecture concerns a uniform bound on maximal proper subgroup…
openfinite-groups subgroup-growth
05
Grigorchuk–Lubotzky–Pyber conjecture on congruence subgroup growth
About 22 years old
Grigorchuk–Lubotzky–Pyber conjecture. The two asymptotic constants coincide and equal
openarithmetic-groups congruence-subgroups subgroup-growth
08
The asymptotic index-subgroup count conjecture for braid groups
About 22 years old
Let $B_n$ be the braid group on $n$ strands, and let $a_k(B_n)$ denote the number of subgroups of index $k$ in $B_n$ . For $n$ sufficiently large, write $c(k/n)$ for a constant depe…
openbraid-groups finite-groups subgroup-growth
010
The subexponential subgroup growth conjecture for pro- $p$ groups
About 18 years old
Subexponential subgroup growth conjecture. If $G$ has subexponential subgroup growth and
openprofinite-groups pro-p-groups subgroup-growth
017

Wall's conjecture on maximal proper subgroups of finite groups