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inside the loop of modules/xoopsmembers/index.php:
$foundusers =& $member_handler->getUsers($criteria, true);
foreach (array_keys($foundusers) as $j) {
around line 344, you should put this:
$userdata['rank'] = $foundusers[$j]->rank;
Then in the template xoopsmembers_searchresult.html, you should add
<td class="odd" align="center"><{$users[i].rank.title}>td>
where you want it to show up.
Note that the rank is an array of id (rank ID, not user ID), title and image so therefore you need that extra .title to get the title.
However, I do want to warn against this, as you will add a database query for each displayed user on that page. Unfortunately, the rank handling is not so well-formed in XOOPS, yet. But if your traffic is not overwhelming, it shouldn't matter _that_ much - just so that you don't complain about it afterwards
