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Preserve more properties in DirectProduct #3053

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Nov 26, 2018
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Preserve more properties in DirectProduct #3053

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3ddd860
gprd.gi: preserve more properties in DirectProduct
wilfwilson Nov 24, 2018
d3c6e9f
gprd.gi: preserve properties in DirectProduct more intelligently
wilfwilson Nov 25, 2018
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10 changes: 7 additions & 3 deletions lib/gprd.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -28,9 +28,13 @@ local d, prop;

# test/set a few properties and attributes from factors

for prop in [IsFinite, IsNilpotentGroup, IsAbelian, IsSolvableGroup] do
if ForAll(arg, Tester(prop)) then
Setter(prop)(d, ForAll(arg, prop));
for prop in [IsFinite, IsNilpotentGroup, IsAbelian, IsSolvableGroup, IsBand,
IsInverseSemigroup, IsRegularSemigroup, IsIdempotentGenerated,
IsLeftZeroSemigroup, IsRightZeroSemigroup, IsZeroSemigroup] do
if ForAny(arg, x -> Tester(prop)(x) and not prop(x)) then
Setter(prop)(d, false);
elif ForAll(arg, x -> Tester(prop)(x) and prop(x)) then
Setter(prop)(d, true);
fi;
od;

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57 changes: 57 additions & 0 deletions tst/testinstall/gprd.tst
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@@ -0,0 +1,57 @@
#############################################################################
##
#W gprd.tst GAP library Wilf A. Wilson
##
##
#Y Copyright (C) 2018, The GAP Group
##
#@local g1,g2,g3,d1,d2,d3,d4
gap> START_TEST("gprd.tst");

# Test that information about IsNilpotentGroup is preserved by DirectProduct
gap> g1 := SymmetricGroup(3);;
gap> IsNilpotentGroup(g1);
false
gap> g2 := CyclicGroup(IsPermGroup, 6);;
gap> IsNilpotentGroup(g2);
true
gap> d1 := DirectProduct(g1, g1);;
gap> HasIsNilpotentGroup(d1) and not IsNilpotentGroup(d1);
true
gap> d2 := DirectProduct(g1, g2);;
gap> HasIsNilpotentGroup(d2) and not IsNilpotentGroup(d2);
true
gap> d3 := DirectProduct(g2, g2);;
gap> HasIsNilpotentGroup(d3) and IsNilpotentGroup(d3);
true
gap> g3 := Group([(1,2), (1,2,3)]);;
gap> d4 := DirectProduct(g3, g3, g3);;
gap> (HasIsNilpotentGroup(g3) and HasIsNilpotentGroup(d4)
> and not IsNilpotentGroup(d4)) or (not HasIsNilpotentGroup(g3) and not
> HasIsNilpotentGroup(d4));
true

# Test that information about IsFinite is preserved by DirectProduct
gap> g1 := SymmetricGroup(3);;
gap> HasIsFinite(g1) and IsFinite(g1);
true
gap> g2 := FreeGroup(1);;
gap> IsFinite(g2);
false
gap> d1 := DirectProduct(g1, g1);;
gap> HasIsFinite(d1) and IsFinite(d1);
true
gap> d2 := DirectProduct(g1, g2);;
gap> HasIsFinite(d2) and not IsFinite(d2);
true
gap> d3 := DirectProduct(g2, g2);;
gap> HasIsFinite(d3) and not IsFinite(d3);
true
gap> g3 := SymmetricGroup(5);;
gap> d4 := DirectProduct(g1, g2, g3);;
gap> HasIsFinite(d4) and not IsFinite(d4);
true

#
gap> STOP_TEST("gprd.tst");