I have it like this: User-agent: * Allow: / Disallow: /article.html Code (markup): My question is: Will Google follow the links that are in that page? I want google to index that page but do not follow the links.
No this would not work for you. You should rather try following meta tag in the page code: <META NAME="ROBOTS" CONTENT="INDEX, NOFOLLOW" />
It does what you want it to do, index the page, but not follow the links. Right now, your robots.txt does not allow articles.html to be crawled or indexed. You should use the meta tag, or use the nofollow attribute on each individual link. The meta tag will be easiest.
The robots.txt is to stop (disallow) search engines visiting certain pages of your website, if they can't visit the page, then they can't index it. As others have said, for allowing pages to be indexed but not following any links on the page, the robots meta tag should be used.
Info About Robot.txt and nofollow.. Robot.txt – This is a file written and stored in the root directory of a website that restricts search engine spiders from indexing certain areas of the website. nofollow: It is an HTML attribute value used to instruct some search engines that a hyperlink should not influence the link target's ranking in the search engine's index. It is intended to reduce the effectiveness of certain types of search engine spam, thereby improving the quality of search engine results and preventing spamdexing from occurring.