Add a few more IsRegularPGroup tests (#5775)

Contributed by Jack Schmidt in a comment on PR #5359.

Also change phrasing in the documentation for IsRegularPGroup.

Author: fingolfin

lib/grp.gd

@@ -488,7 +488,7 @@ InstallTrueMethod( IsPowerfulPGroup, IsFinite and IsPGroup and IsAbelian );
 ##
 ##  <Description>
 ##  <Index Key="RegularPGroup">Regular <M>p</M>-group</Index>
-##  A finite <M>p</M>-group <A>G</A> is said to be a <E>regular <M>p</M>-group</E>
+##  A finite <M>p</M>-group <A>G</A> is a <E>regular <M>p</M>-group</E>
 ##  if for all <M>a,b</M> in <A>G</A>, one has <M>a^p b^p = (a b)^p c^p</M>
 ##  where <M>c</M> is an element of the derived subgroup of the group generated
 ##  by <M>a</M> and <M>b</M> (see&nbsp;<Cite Key="Hal34"/>).

tst/testinstall/pgroups.tst

@@ -222,5 +222,29 @@ gap> Number(myList,IsRegularPGroup);
 5
 gap> g:=AbelianGroup(ListWithIdenticalEntries(2000,2));;
 
+#
+# Test IsRegularPGroup method thoroughly
+#
+gap> IsRegularPGroup(SmallGroup(8, 3)); # Case 1
+false
+gap> IsRegularPGroup(SmallGroup(2187, 224)); # Case 2
+false
+gap> IsRegularPGroup(SmallGroup(27,3)); # Case 3
+true
+gap> IsRegularPGroup(SmallGroup(81, 1)); # Case 4
+true
+gap> IsRegularPGroup(SmallGroup(243,22)); # Case 5
+true
+gap> IsRegularPGroup(SmallGroup(2187, 4487)); # Case 6
+true
+gap> IsRegularPGroup(SmallGroup(81, 7)); # Case 7
+false
+gap> IsRegularPGroup(SmallGroup(78125, 684)); # Case 8
+true
+gap> IsRegularPGroup(SmallGroup(243, 51)); # Case 10 (no case 9 found)
+false
+gap> IsRegularPGroup(SmallGroup(2187, 663)); # Case 11, takes 3 seconds
+true
+
 #
 gap> STOP_TEST("pgroups.tst", 1);