It is not allowed to place a <a> link element inside a <button> element. Some browsers will actually do what you want, and some won't. If you must have a button that acts as a link, there are two solutions:
Style the link
Use only the <a> element and use CSS to style it like a button (which you have indicated you don't want).
Wrap button in form
Wrap the <button> in a <form> and set the link target as the form's action attribute:
<form action="https://www.google.com">
<input type="submit" value="Google it!" />
</form>