Assuming the data is sorted as shown, there's no need for a hash. You just have to keep track of the value from the previous row.

my $prev;
while (<$fh>) {
    my ($field1, $field2) = split;

    if (!defined($prev) || $prev ne $field2) {
        print("\n") if !defined($prev);
        $prev = $field2;
        print("$field2\n");
    }

    print("$field1\n");
}
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