In two places you repeat the code:

my $group_name = get_input("Enter Group Name: ");
if ( exists $group_name->{$group_name} ) {
[download]

The sub get_input() returns a string which, as the error messages are telling you, you are trying to use as hash reference with exists. On the left side of the -> arrow $group_name is a hash reference and on the right side of the arrow it is a string and key to the hash. It looks like in read_doc you need to create a hash of groups and return a reference to it.