How to group buttons in different forms tags in Bootstrap

You can use JQuery to achieve it.

<form id="form1" action="search.php" method="POST">
 <input type="hidden" name="some name" value="same value">
</form>

<form id="form2" action="edit_product.php" method="post">
 </form>

<div class="btn-group"> 
 <button id="more" style="float:left" class="btn" type="submit"><i class="icon-search"></i>  More</button><!--More button-->
 <button id="edit" class="btn btn-primary" type="submit"  name="product_number" value="some value"><i class="icon-cog icon-white"></i> Edit</button>
 <button data-toggle="modal" href="#error_delete" class="btn btn-danger"><i class="icon-trash icon-white"></i> Delete</button>    
</div>

And with JQuery:

$("#more").click(function() {
    $("#form1").submit();
}

If you'd rather not use scripting you can use hidden inputs (or any inline element, such as <i></i>) to create the proper first:child and last:child relationships:

Fiddle demo

<form class="btn-group">
    <button class="btn">Button One</button>
    <input type="hidden" class="btn"><!-- fake sibling to right -->
</form>

<form class="btn-group">
    <i></i><!-- fake sibling to left -->
    <button class="btn">Button Two</button>
</form>

In the latest versions of Bootstrap 2 I did have to add one bit of CSS override:

form.btn-group + form.btn-group {margin-left: -5px;}