BuddyPress.org

A child theme contain usually
style.css
functions.php

To make it work with BP, you add a copy of the original page.php of 2014 and rename it buddypress.php

2014 comes also with a full-width template which is in page-templates folder.
If you compare both files, you will see that the only difference is at line 40 of page.php
get_sidebar( 'content' );

To get what you want, you simply add a conditionnal to this part.

if( !bp_is_groups_component() ) { 
   get_sidebar( 'content' );
}

That said, i think it’s not necessary, as with or without this hack, BP’s content comes full-width on 2014. At least and by default, in the whole white zone, right of the left black sidebar. Also remind that 2014 is a left aligned theme, which can let think that you have a lot of space on the right, specially on a large desktop screen.

With 2012, it’s a bit different, as this theme use a class called full-width, directly in the html. To use the same technique, we have to echo the div to get the condition to work properly.
And 2013 doesn’t use a full-width template.

<?php if( !bp_is_groups_component() ) { 
       echo '<div id="content" role="main">';
 } else { 
echo '<div id="content" class="full-width" role="main">';
 } ?>

grr – typos at midnight… should be NOW that I am digging deeper into 2014,,

you could (although this theme is quite tricky with the various sizing things, and I am NOT an expert with this theme or css – so make backups, use child themes – all that jazz)

you could try changing (or overwriting with child theme / enque an overlap style sheet)

@media screen and (min-width: 1218px) {
.site-content, .site-main .widecolumn {
    margin-left: 222px;
}
}

to:

@media screen and (min-width: 1218px) {
.site-content, .site-main .widecolumn {
    margin-left: 90px;
}
}

and..

.buddypress .site-content article .entry-content, .buddypress .site-content article .entry-header {
    max-width: 100%;
    padding: 0px 10% 5%;
}

change to

.buddypress .site-content article .entry-content, .buddypress .site-content article .entry-header {
    padding: 0px 1% 5%;
}

– now of course how these settings affect the groups page is one thing this could cause ill effects on other pages – (ones with double sidebars) – and at different screen sizes.. this 2014 thing gets pretty picky..

especially with 2014 doing one thing, and the bp-addon style thing doing some other things.. one percentage change here looks good – but a different page at a difference screen size – grrr.. you have to test a lot with this mix (come to find out the hard way here the past couple weeks!)

This will add a lot more space, which is what I guess you are going for in general – but not remove all sidebars..
and
That does not get rid of the left sidebar, which is I guess what you were meaning to ask in the first place with this thread (and I think everyone else was assuming you wanted to get rid of the right sidebar, as our understanding of the term “full width page” – err template in my mind is just that.. looks like you really want a “no sidebars at all page template” for groups page?