Introduce associativity check to AsSemigroup

See #4030.

I thought about adding a similar check to `SemigroupByGenerators`,
but that operation is explicitly documented as not checking for
associativity.

Fixes #4030.

lib/semigrp.gi

@@ -542,7 +542,25 @@ InstallMethod( AsSemigroup,
     "generic method for collections",
     [ IsCollection ],
     function ( D )
-    local   S,  L;
+    local L, S, i, j, k;
+
+    # Must check associativity
+    if ApplicableMethod(IsAssociative, [D]) <> fail then
+      # In case there are better methods/known attributes for associativity
+      if not IsAssociative(D) then
+        return fail;
+      fi;
+    else
+      for i in D do
+        for j in D do
+          for k in D do
+            if (i * j) * k <> i * (j * k) then
+              return fail;
+            fi;
+          od;
+        od;
+      od;
+    fi;
 
     D := AsSSortedList( D );
     L := ShallowCopy( D );

tst/testbugfix/2021-04-08-non-associative-semigroup.tst

@@ -0,0 +1,19 @@
+# https://github.com/gap-system/gap/issues/4030
+gap> T := [
+>   [ 1, 2, 6, 5, 4, 3 ],
+>   [ 2, 1, 4, 2, 2, 5 ],
+>   [ 6, 5, 1, 6, 6, 4 ],
+>   [ 5, 6, 3, 4, 1, 2 ],
+>   [ 4, 3, 2, 1, 5, 6 ],
+>   [ 3, 4, 5, 3, 3, 1 ]
+> ];;
+gap> M := MagmaByMultiplicationTable(T);
+<magma with 6 generators>
+gap> IsAssociative(M);
+false
+gap> AsSemigroup(M);
+fail
+gap> M := MagmaByMultiplicationTable(T);
+<magma with 6 generators>
+gap> AsSemigroup(M);
+fail