Is it true that Google doesn't recognize a corporate website's blog?
that is integrated in the website. I think I read about it somewhere but can't find it now.
for example: www.abcdegf.com/blog
will it be recognized by the Google search engine?
A Blog in a sub-directory will still be indexed, it's possible that it may not receive the same priority as if on the root of a domain name.
Of course some companies may choose to not make certain blogs appear in searches, by using a noIndex instruction in a robot.txt file.