twitter-bootstrap: how to get rid of underlined button text when hovering over a btn-group within an <a>-tag?

{ text-decoration: none !important}

EDIT 1:

For you example only a{text-decoration: none} will works

You can use a class not to interfere with the default behaviour of <a> tags.

<a href="#" class="nounderline">
  <div class="btn-group">
    <button class="btn">Text</button>
    <button class="btn">Text</button>
  </div>
</a>

CSS:

.nounderline {
  text-decoration: none !important
}

Bootstrap 4+

This is now easy to do in Bootstrap 4+

<a href="#" class="text-decoration-none">
    <!-- That is all -->
</a>

Buttons with the btn class do not have underlines unless you are doing something wrong: In this case nesting <button> inside of <a>^†.

Something that I think you might be trying to do, is to create a bootstrap button without any decorations (underline, outline, button borders, etc). In other words, if your anchor is not a hyperlink, it is semantically a button.

Bootstrap's existing btn class appears to be the correct way to remove underline decorations from anchor buttons:

Use the button classes on an <a>, <button>, or <input> element

EDIT: Hitesh points out that btn will give you a shadow on :active. Thanks! I have modified my first example to use btn-link and incorporated the accepted answer's text-decoration: none to avoid this problem. Note that nesting a button inside of an anchor remains malformed html^†, a point which isn't addressed by any of the other answers.

<link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.5/css/bootstrap.css" rel="stylesheet"/>
<div>
    <!-- use anchors for borderless buttons -->
    <a href="#" class="btn btn-link" style="text-decoration: none">Text</a> 
    <a href="#" class="btn btn-link" style="text-decoration: none">Text</a>
</div>

Alternatively, for a regular button group using anchors:

<link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.5/css/bootstrap.css" rel="stylesheet"/>
<div class="btn-group">
    <!-- use anchors for borderless buttons -->
    <a href="#" class="btn btn-default">Text</a> 
    <a href="#" class="btn btn-default">Text</a>
</div>

In other words, it should not be necessary to introduce your own nounderline class and/or custom styling as the other answers suggest. However, be aware of certain subtleties.

^† According to the HTML5 spec, <a><button>..</button></a> is illegal:

Content model: Transparent, but there must be no interactive content descendant.

...

Interactive content is content that is specifically intended for user interaction. a, audio (if the controls attribute is present), button, embed, iframe, img (if the usemap attribute is present), input (if the type attribute is not in the hidden state), keygen, label, object (if the usemap attribute is present), select, textarea, video (if the controls attribute is present)

P.S. If, conversely, you wanted a button that has underline decorations, you might have used btn-link. However, that should be rare - this is almost always just an anchor instead of a button!