$string =~ s/(\S+)\.\1/'$1.$1'/g;    # Add quotes

and plugged into merlyn's reply

$_ = join(".", sort split(/\./, "Pugh.Barney.Pugh.Barney.McGrew.Cuthbert.Dibble.Grub"));
$_ =~ s/(\S+)\.\1/'$1.$1'/g;	  # Add quotes
my @keepers = grep defined $_, /'(.*?)'|([^.]+)/g;
print map "$_\n", @keepers;