-
Notifications
You must be signed in to change notification settings - Fork 162
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
1 parent
3cc245a
commit e1b3267
Showing
1 changed file
with
171 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,171 @@ | ||
| gap> START_TEST("pgroups.tst"); | ||
| gap> A := Group((1,2),(3,4),(5,6)); | ||
| Group([ (1,2), (3,4), (5,6) ]) | ||
| gap> G := DirectProduct(A, A); | ||
| Group([ (1,2), (3,4), (5,6), (7,8), (9,10), (11,12) ]) | ||
| gap> IsPGroup(G); | ||
| true | ||
| gap> HasPrimePGroup(A) and HasPrimePGroup(G); | ||
| true | ||
| gap> PrimePGroup(A); | ||
| 2 | ||
| gap> PrimePGroup(G); | ||
| 2 | ||
| gap> B := Group((1,2,3),(4,5,6)); | ||
| Group([ (1,2,3), (4,5,6) ]) | ||
| gap> IsAbelian(B); | ||
| true | ||
| gap> G := DirectProduct(B, B); | ||
| Group([ (1,2,3), (4,5,6), (7,8,9), (10,11,12) ]) | ||
| gap> IsPGroup(G); | ||
| true | ||
| gap> HasPrimePGroup(G); | ||
| true | ||
| gap> PrimePGroup(G); | ||
| 3 | ||
| gap> C := Group((1,2,3,4),(5,6,7,8)); | ||
| Group([ (1,2,3,4), (5,6,7,8) ]) | ||
| gap> IsAbelian(C); | ||
| true | ||
| gap> G := DirectProduct(C, C); | ||
| Group([ (1,2,3,4), (5,6,7,8), (9,10,11,12), (13,14,15,16) ]) | ||
| gap> Size(G); | ||
| 256 | ||
| gap> IsPGroup(G); | ||
| true | ||
| gap> HasPrimePGroup(G); | ||
| true | ||
| gap> PrimePGroup(G); | ||
| 2 | ||
| gap> D := Group((1,3),(1,2,3,4)); | ||
| Group([ (1,3), (1,2,3,4) ]) | ||
| gap> G := DirectProduct(D, D); | ||
| Group([ (1,3), (1,2,3,4), (5,7), (5,6,7,8) ]) | ||
| gap> IsPGroup(G); | ||
| true | ||
| gap> HasPrimePGroup(D) and HasPrimePGroup(G); | ||
| true | ||
| gap> PrimePGroup(D); | ||
| 2 | ||
| gap> PrimePGroup(G); | ||
| 2 | ||
| gap> Q := Group( (1,2,3,8)(4,5,6,7), (1,7,3,5)(2,6,8,4) ); | ||
| Group([ (1,2,3,8)(4,5,6,7), (1,7,3,5)(2,6,8,4) ]) | ||
| gap> SetIsPGroup(Q,true); | ||
| gap> PrimePGroup(Q); | ||
| 2 | ||
| gap> G := DihedralGroup(IsFpGroup, 8); | ||
| <fp group of size 8 on the generators [ r, s ]> | ||
| gap> IsPGroup(G); | ||
| true | ||
| gap> H := CyclicGroup(IsFpGroup, 2); | ||
| <fp group of size 2 on the generators [ a ]> | ||
| gap> hom := GroupHomomorphismByImages(G, H, [G.1, G.2], [H.1, One(H)]); | ||
| [ r, s ] -> [ a, <identity ...> ] | ||
| gap> K := Kernel(hom); | ||
| Group(<fp, no generators known>) | ||
| gap> SetIsPGroup(K, true); | ||
| gap> PrimePGroup(K); | ||
| 2 | ||
| gap> IsPGroup(TrivialGroup()); | ||
| true | ||
| gap> PrimePGroup(TrivialGroup()); | ||
| fail | ||
| gap> IsPGroup(AbelianGroup([2, 4, 8, 16])); | ||
| true | ||
| gap> IsPGroup(AbelianGroup([2, 4, 8, 18])); | ||
| false | ||
| gap> H1 := Group((1,2)(3,4),(1,2,3)); | ||
| Group([ (1,2)(3,4), (1,2,3) ]) | ||
| gap> IsPGroup(H1); | ||
| false | ||
| gap> H2 := Group((1,2),(3,4,5)); | ||
| Group([ (1,2), (3,4,5) ]) | ||
| gap> IsPGroup(H2); | ||
| false | ||
| gap> H3 := Group((1,2),(3,4,5)); | ||
| Group([ (1,2), (3,4,5) ]) | ||
| gap> IsAbelian(H3); | ||
| true | ||
| gap> IsPGroup(H3); | ||
| false | ||
| gap> H4 := Group((1,2),(3,4,5)); | ||
| Group([ (1,2), (3,4,5) ]) | ||
| gap> IsAbelian(H4); | ||
| true | ||
| gap> Size(H4); | ||
| 6 | ||
| gap> IsPGroup(H4); | ||
| false | ||
| gap> K := Group((1,3),(1,2,3,4),(5,6,7)); | ||
| Group([ (1,3), (1,2,3,4), (5,6,7) ]) | ||
| gap> IsNilpotentGroup(K); | ||
| true | ||
| gap> HasIsPGroup(K); | ||
| true | ||
| gap> IsPGroup(K); | ||
| false | ||
| gap> L := Group((2,4), (1,2,3,4)); | ||
| Group([ (2,4), (1,2,3,4) ]) | ||
| gap> IsNilpotentGroup(L); | ||
| true | ||
| gap> HasIsPGroup(L) and HasPrimePGroup(L); | ||
| true | ||
| gap> IsPGroup(L); | ||
| true | ||
| gap> PrimePGroup(L); | ||
| 2 | ||
| gap> F := FreeGroup("r","s"); | ||
| <free group on the generators [ r, s ]> | ||
| gap> r := F.1; s := F.2; | ||
| r | ||
| s | ||
| gap> G := F/[ r^4, s^2, s*r*s*r ]; | ||
| <fp group on the generators [ r, s ]> | ||
| gap> IsNilpotentGroup(G); | ||
| true | ||
| gap> G := F/[ r^3, s^2, r*s*r*s ]; | ||
| <fp group on the generators [ r, s ]> | ||
| gap> IsNilpotentGroup(G); | ||
| false | ||
| gap> ForAll(List([1..11], i -> TransitiveGroup(8,i)), IsPGroup); | ||
| true | ||
| gap> IsPGroup(TransitiveGroup(8, 12)); | ||
| false | ||
| gap> IsNilpotentGroup(TransitiveGroup(8, 12)); | ||
| false | ||
| gap> IsPGroup(AlternatingGroup(3)); | ||
| true | ||
| gap> IsPGroup(AlternatingGroup(4)); | ||
| false | ||
| gap> IsPGroup(SymmetricGroup(3)); | ||
| false | ||
| gap> G := SymmetricGroup(8); | ||
| Sym( [ 1 .. 8 ] ) | ||
| gap> s := Size(G); | ||
| 40320 | ||
| gap> IsPGroup(G); | ||
| false | ||
| gap> IsNilpotentGroup(G); | ||
| false | ||
| gap> ForAll(PrimeDivisors(s), p -> HasIsPGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> ForAll(PrimeDivisors(s), p -> HasPrimePGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> ForAll(PrimeDivisors(s), p -> p=PrimePGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> G := DihedralGroup(Factorial(8)); | ||
| <pc group of size 40320 with 11 generators> | ||
| gap> IsPGroup(G); | ||
| false | ||
| gap> IsNilpotentGroup(G); | ||
| false | ||
| gap> s := Size(G); | ||
| 40320 | ||
| gap> ForAll(PrimeDivisors(s), p -> HasIsPGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> ForAll(PrimeDivisors(s), p -> HasPrimePGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> ForAll(PrimeDivisors(s), p -> p=PrimePGroup(SylowSubgroup(G, p))); | ||
| true | ||
| gap> STOP_TEST("pgroups.tst", 10000); |