## Groups of degree 10 that do not satisfy the universal transversal property ## ## GAP log file gap> g:=[PrimitiveGroup(10, 1), PrimitiveGroup(10,2), PrimitiveGroup(10, 3), > PrimitiveGroup(10, 4), PrimitiveGroup(10, 5), PrimitiveGroup(10, 6), > PrimitiveGroup(10, 7)];; gap> o:=Orb(g[1], [ 1, 2, 3 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 1, 2, 2, 3, 3, 3, 3, 3, 3 ])); false gap> o:=Orb(g[2], [ 1, 2, 3 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 1, 2, 2, 3, 3, 3, 3, 3, 3 ])); false gap> o:=Orb(g[3], [ 1, 2, 3, 10 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 2, 3, 3, 4, 4, 4, 4, 1, 1 ])); false gap> o:=Orb(g[4], [ 1, 2, 3, 10 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 2, 3, 4, 4, 4, 4, 1, 1, 1 ])); false gap> o:=Orb(g[5], [ 1, 2, 3, 10 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 2, 3, 3, 4, 4, 4, 4, 1, 1 ])); false gap> o:=Orb(g[6], [ 1, 2, 3, 10 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 2, 3, 4, 4, 4, 4, 1, 1, 1 ])); false gap> o:=Orb(g[7], [ 1, 2, 3, 10 ], OnSets);; Enumerate(o);; gap> ForAny(o, x-> IsInjectiveListTrans(x, [ 1, 2, 3, 4, 4, 4, 4, 1, 1, 1 ])); false