You can do it with one regexp actually:

use warnings;
use strict;

$_ = join"", <DATA>;

while(/^B\s+(\w+)\s+(\w+)\s+(ONLINE)(?=.*^G\s+\1\b)/msg)
{
    print "Group '$1' is frozen on host '$2'.\n"
}    

__DATA__
B  group1      host1       ONLINE
B  group1      host2       OFFLINE
B  group2      host2       ONLINE
B  group2      host3       OFFLINE
B  group3      host3       ONLINE
B  group4      host1       ONLINE
B  group5      host3       ONLINE
G group2
G group3
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