Angharad,
What you want to use is a high water mark algorithm per item. It would look something like this:

#!/usr/bin/perl
use strict;
use warnings;

my $input = $ARGV[0] or die "Usage: $0 <input>";
open(my $fh, '<', $input) or die "Unable to open '$input' for reading:
+ $!";

my %high;
while (<$fh>) {
    chomp;
    my ($item, $group, $count) = split ' ';
    $high{$item} = $count if ! defined $high{$item} || $count > $high{
+$item};
}
for my $item (keys %high) {
    print "$item high count was $high{$item}\n";
}
[download]

I have purposely left this code not working exactly as required (group is omitted) to give you something to work towards. If you need more help - remember that the entire line is stored in $_ Also, this assumes that counts will always be numeric and that they will be whitespace delimited. For something much more fancy, have a look at How A Function Becomes Higher Order

Update: You didn't mention what should happen if an item has more than one group with the same highest count. The algorithm can be modified to handle the first/last/all/random values in that situation but you will need to determine what is right for you.