No infinite loop here. But is this really what you wanted?

use Data::Dumper;

my @line= qw(a b c);
my @angel=qw(1 2 b);

for ( $i = 1 ; $i <= $#line ; $i++ ) {
       $k = $line[$i];
       for ( $v = 1 ; $v <= $#angel ; $v++ ) {
           $j = $angel[$v];
           if ( $k =~ m/($j)/i ) {
               push ( @a, $v );
           }
           else { push ( @b, $v ); }
       }
   }
print Dumper(\@a, \@b);
[download]

prints out:

$VAR1 = [
          2
        ];
$VAR2 = [
          1,
          1,
          2
        ];
[download]

BTW: Arrays start at 0 not at 1...