Are there infinitely many insipid numbers?Are There Primes of Every Hamming Weight?Central numbers and de Polignac's conjectureDoes the hyperoctahedral group have only 3 maximal normal subgroups?Are the distributive permutation groups linearly primitive?Are the finite groups inclusions, almost all relatively cyclic?Large subgroups of $S_n$ without large symmetric or alternating subgroupsWhen does the first subgroup growth function grow?Is there a subgroup of dual depth 3?Existence of infinitely many number fields with bounded class numberThe sporadic numbers
Are there infinitely many insipid numbers?
Are There Primes of Every Hamming Weight?Central numbers and de Polignac's conjectureDoes the hyperoctahedral group have only 3 maximal normal subgroups?Are the distributive permutation groups linearly primitive?Are the finite groups inclusions, almost all relatively cyclic?Large subgroups of $S_n$ without large symmetric or alternating subgroupsWhen does the first subgroup growth function grow?Is there a subgroup of dual depth 3?Existence of infinitely many number fields with bounded class numberThe sporadic numbers
$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_r to inftyr/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
add a comment |
$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_r to inftyr/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
add a comment |
$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_r to inftyr/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_r to inftyr/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
8,7884 gold badges40 silver badges110 bronze badges
add a comment |
add a comment |
1 Answer
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$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 6 hours ago
verretverret
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$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 6 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
2,1171 gold badge13 silver badges24 bronze badges
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