Submit primefaces table after select - ajax

Question

I have a table in Primefaces with a single selection. After the user selects an entry of that table, the whole form should be submitted. I could use a commandbutton to sumbit, but I don't want the user to do this, cause the selection is the last and final step of the form.
<p:dataTable value="#{bean.selectedItems}" var="selItem"
selection="#{bean.selectedItem}"
rowKey="#{selItem.id}"
selectionMode="single"
id="selectedTbl">
<p:ajax event="rowSelect" listener="#{bean.onSelectListener}"/>
<p:column selectionMode="single"/>
...
<p:dataTable/>
The ajax listener as well as the set method of the selectedItem is called, but how do I trigger a submit from ajax?
Update: More detailed example
Case: Only one person per group can be enabled. The user has to decide based on many information in a table. And sometimes the user has to do this very often.
<h:form>
<p:selectOneMenu value="#{bean.group}" valueChangeListener="#{bean.onGroupChange}">
<f:selectItem itemLabel="Select..." noSelectionOption="true"/>
<f:selectItems value="#{bean.groups}"/>
<p:ajax update="selectedTbl"/>
</p:selectOneMenu>
<p:dataTable value="#{bean.selectedItems}" var="selItem"
selection="#{bean.selectedItem}"
rowKey="#{selItem.id}"
selectionMode="single"
id="selectedTbl">
<p:ajax event="rowSelect" listener="#{bean.onSelectListener}"/>
<p:column selectionMode="single"/>
<p:column headerText="ID">
<h:outputText value="selItem.id"/>
</p:column>
<p:column headerText="Name">
<h:outputText value="selItem.name"/>
</p:column>
<!--Some more Information about the person, based on the the user makes a decision.-->
<p:dataTable/>
<!--only one User per Group can be enabled-->
<p:commandButton value="Enable" action="#{bean.enableSelected}" onclick="submit()"/>
</h:form>
bean:
public void enableSelected(){
manager.modifyPerson(selectItem);
selectedItems.clear();
selectedItem = null;
group = null;
}
public void onSelectListener(SelectEvent event){
selectedItem = (Person) event.getObject();
}
The bean is pretty simple only getter and setter. The onGroupChange Method loads new values for selectItems from the db.
I want to get rid of the commandbutton and move the functionality from enableSelected to onSelectListener. When I move the db-Function to enableSelected it works but the page isn't refreshed.
When I add update="#form" to ajax it doesn't work so I wanted to use submit().

Answer 1

Try to add process="#form" in your ajax.
<p:ajax event="rowSelect" process="#form" listener="#{bean.onSelectListener}"/>