If we wanted to match a single character, our pattern would be /a./. The control character is a '.' after the letter in question.
No! /a./ means match two characters, an 'a' followed by any other character. To match a single lower-case 'a', the pattern is simply /a/ - try it and see:
$_ = 'He lives in Liberia';
print 'with dot: ', $_ if /a./;
# No output
print 'without dot: ', $_ if /a/;
# Outputs 'without dot: He lives in Liberia'
Also, in your last paragraph, you've inverted your square brackets and slashes...
To clarify, the dot (period) is not a 'control character', as you seem to imagine, but a 'wildcard character'. To quote from perlretut
(which I highly recommend you read, and include in your list of other sources):
The period '.' matches any character but "\n"
Update2: s/perlreftut/perlretut, sorry!