I read in a book that "however" is a conjunction. Does that mean if I wrote: However, he was wrong. That would be a sentence fragment? Thanks.
Check a dictionary, and you will see that however can be either a conjunction or an adverb. In the sentence above, it is used as an adverb. You should always look at a dictionary first for this kind of question. Many common words take on different parts of speech for different meanings and contexts.
you can get a much quicker and more detailed answer to such questions, by keeping a good online dictionary in your favorites menu and consulting that, before asking them of folks here... you'll find a link to the one i use, along with links to other helpful writing resources, in the sticky at the top of this section...