<f:view>
    <a4j:form>
    ....
    <h:selectOneMenu style="width:100px" value="#{userSessionBean.simpleDictPreffix}" id="dict-preffix"
                     valueChangeListener="#{userSessionBean.dictPreffixListValueChanged}">
        <f:selectItems value="#{applicationData.searchList}"/>
        <a4j:support event="onchange" ajaxSingle="true" action="#{userSessionBean.changeDictionaryAction}"
                     reRender="btnPanel"/>
    </h:selectOneMenu>
    ....
    <a4j:outputPanel rendered="#{userSessionBean.showDictBtnVisible}" id="btnPanel">
        <a4j:commandButton value="..." title="#{header_var.dict_btn_tip}"
                           action="#{userSessionBean.showDictAction}"
                           reRender="mpViewSearchValues"
                           rendered="#{userSessionBean.showDictBtnVisible}"
                           id="showDictBtn"/>
    </a4j:outputPanel>
</a4j:form>
</f:view>

        public String changeDictionaryAction() {
            ExternalContext ec = FacesContext.getCurrentInstance().getExternalContext();

            List<SearchItemDescriptor> searchItemList = (List<SearchItemDescriptor>) ec.getApplicationMap().get("search-list");

            for (SearchItemDescriptor sid : searchItemList) {
                String s = sid.getPreffix();

                if (s.equals(simpleDictPreffix) == true) {
                    if (sid.getMenu() != null) {
                        showDictBtnVisible = true;

                        return null;
                    }
                }
            }

            showDictBtnVisible = false;

            return null;
        }