In Bootstrap 3 you could easily remove the "caret" (small arrow that points down) from a dropdown button, I can't see how to do it in Bootstrap 4 though because they no longer use <span class="caret"></span>
.
<div class="input-group mb-3">
<div class="input-group-prepend">
<button class="btn btn-outline-secondary dropdown-toggle" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Dropdown</button>
<div class="dropdown-menu">
<a class="dropdown-item" href="#">Action</a>
<a class="dropdown-item" href="#">Another action</a>
<a class="dropdown-item" href="#">Something else here</a>
<div role="separator" class="dropdown-divider"></div>
<a class="dropdown-item" href="#">Separated link</a>
</div>
</div>
<input type="text" class="form-control" aria-label="Text input with dropdown button">
</div>
It's done in css. Do something like that:
.dropdown-toggle:after { content: none }