Recog An/Sn unknown degree: conder, holt #265
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,45 +1,64 @@ | ||
| # | ||
| # For each entry (d, k) we construct Sym(d)/Alt(d) acting on k-sets. | ||
| # For each entry (d, k), we must have 2 * k ^ 2 > d, | ||
| # otherwise LargeBasePrimitive recognises the group instead of SnAnUnknownDegree. | ||
| gap> dataPerm := [[5, 2], [7, 2], [8, 3], [9, 3], [10, 3], [11, 3], [12, 3], [13, 3]];; | ||
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| # | ||
| # PermGroup action on k-sets | ||
| gap> PermOnKSets := function(G, k) | ||
| > local sets; | ||
| > sets := Combinations([1 .. NrMovedPoints(G)], k);; | ||
| > return Action(G, sets, OnSets);; | ||
| > end;; | ||
| gap> AltOnKSets := function(d, k) | ||
| > return PermOnKSets(AlternatingGroup(d), k); | ||
| > end;; | ||
| gap> SymOnKSets := function(d, k) | ||
| > return PermOnKSets(SymmetricGroup(d), k); | ||
| > end;; | ||
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| # | ||
| gap> altPermGroups := List(dataPerm, entry -> AltOnKSets(entry[1], entry[2]));; | ||
| gap> symPermGroups := List(dataPerm, entry -> SymOnKSets(entry[1], entry[2]));; | ||
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| # | ||
| gap> dataMat := [[5, 4], [7, 3], [8, 5], [11, 7]];; | ||
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| # | ||
| # Permutation Matrix Group | ||
| gap> PermMatGroup := function(G, q) return Group(List( | ||
| > GeneratorsOfGroup(G), | ||
| > x -> ImmutableMatrix(q, PermutationMat(x, NrMovedPoints(G), GF(q))) | ||
| > )); end;; | ||
| gap> AltMatGroup := function(n, q) return PermMatGroup(AlternatingGroup(n), q); | ||
| > end;; | ||
| gap> SymMatGroup := function(n, q) return PermMatGroup(SymmetricGroup(n), q); | ||
| > end;; | ||
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| # | ||
| gap> altMatGroups := List(dataMat, entry -> AltMatGroup(entry[1], entry[2]));; | ||
| gap> symMatGroups := List(dataMat, entry -> SymMatGroup(entry[1], entry[2]));; | ||
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| # | ||
| gap> nonAltOrSymGroups := [ | ||
| > PSL(3, 5), | ||
| > SL(3, 5), | ||
| > Omega(1, 4, 3), | ||
| > ];; | ||
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| # Test | ||
| gap> for i in [1 .. Length(dataPerm)] do | ||
| > RECOG.TestGroup(altPermGroups[i], false, Factorial(dataPerm[i, 1])/2, rec()); | ||
| > RECOG.TestGroup(symPermGroups[i], false, Factorial(dataPerm[i, 1]), rec()); | ||
| > od; | ||
| gap> for i in [1 .. Length(dataMat)] do | ||
| > RECOG.TestGroup(altMatGroups[i], false, Factorial(dataMat[i, 1])/2, rec()); | ||
| > RECOG.TestGroup(symMatGroups[i], false, Factorial(dataMat[i, 1]), rec()); | ||
| > od; | ||
| gap> for i in [1 .. Length(nonAltOrSymGroups)] do | ||
| > ri := RecogNode(nonAltOrSymGroups[i]); | ||
| > if FindHomMethodsGeneric.SnAnUnknownDegree(ri, Grp(ri)) = Success then | ||
| > Print("ERROR: Recognised group [", i, "] wrongly as Sn/An!\n"); | ||
| > fi; | ||
| > od; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,103 @@ | ||
| # RECOG.IsFixedPoint | ||
| gap> ri := RecogNode(SymmetricGroup(10));; | ||
| gap> g := (1,2,3,4,5,6,7,8);; | ||
| gap> c := (1,2,3);; | ||
| gap> r := (1,2)(4,5,6);; | ||
| gap> RECOG.IsFixedPoint(ri, g,c,r); | ||
| true | ||
| gap> r := (2,3,4);; | ||
| gap> RECOG.IsFixedPoint(ri, g,c,r); | ||
| false | ||
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| # RECOG.AdjustCycle | ||
| gap> ri := RecogNode(SymmetricGroup(10));; | ||
| gap> g := (1,2,3,4,5,6,7,8);; | ||
| gap> c := (1,2,3);; | ||
| gap> r := (4,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5) | ||
| gap> r := (3,4,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,4,5) | ||
| gap> r := (2,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5) | ||
| gap> r := (2,4,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5,4) | ||
| gap> r := (2,3,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,4,5) | ||
| gap> r := (1,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5) | ||
| gap> r := (1,4,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5,4) | ||
| gap> r := (1,3,4,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,6,4,5) | ||
| gap> r := (1,2,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5,4) | ||
| gap> r := (1,2,3,5);; | ||
| gap> RECOG.AdjustCycle(ri, g, c, r, 8); | ||
| (3,5,4,6) | ||
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| # RECOG.BuildCycle | ||
| gap> ri := RecogNode(SymmetricGroup(10));; | ||
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| # c = (u,v,w) | ||
| gap> c := (1,2,3);; | ||
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| # Form 1: x = (v,a_1,...,a_alpha) * (w,b_1,....,b_beta) * (...) | ||
| # alpha - beta = 0 | ||
| gap> x := (2,4,5,6)* (3,7,8,9);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = -1 | ||
| gap> x := (2,4,5,6)* (3,7,8,9,10);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = 1 | ||
| gap> x := (2,4,5,6,10)* (3,7,8,9);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = -2 | ||
| gap> x := (2,4,5) * (3,7,8,9,10);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,10,9), 9 ] | ||
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| # alpha - beta = 2 | ||
| gap> x := (2,4,5,6,10) * (3,7,8);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,10), 9 ] | ||
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| # Form 2: x = (v,a_1,...,a_alpha,w,b_1,....,b_beta) * (...) | ||
| # alpha - beta = 0 | ||
| gap> x := (2,4,5,6,3,7,8,9);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = -1 | ||
| gap> x := (2,4,5,6,3,7,8,9,10);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = 1 | ||
| gap> x := (2,4,5,6,10,3,7,8,9);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,9), 9 ] | ||
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| # alpha - beta = -2 | ||
| gap> x := (2,4,5,3,7,8,9,10);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,10,9), 9 ] | ||
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| # alpha - beta = 2 | ||
| gap> x := (2,4,5,6,10,3,7,8);; | ||
| gap> RECOG.BuildCycle(ri, c, x, 10); | ||
| [ (1,2,3,4,7,5,8,6,10), 9 ] |
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Could this be filled in by someone? At which university was this thesis written; what kind of thesis was it?
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I talked to @aniemeyer and learned that this was a thesis in Auckland, but I didn't find something initially. But now it seems this was indeed a B.Sc. thesis there, and it was written by @jonathan-conder . I have now pinged them, and will also write an email. Perhaps we get permissions to post the thesis somewhere, or perhaps Jonathan is willing to put it on e.g. the arXiv (I am not sure if they accept such things, but it seems to contain original research, and they definitely have at least phd theses?)
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Jonathan replied to my email and generously gave permission to share copies of his thesis, and he also made it available at https://jonathan-conder.github.io/afpg.pdf -- this should keep working for the foreseeable future, and I also made sure archive.org has a snapshot. Still, we should probably see if we can also get this onto e.g. Zenodo or so.
Anyway, that gives us enough info to complete this bib record. I'll do so eventually (if nobody beats me to it).