Can we give permission for a group for editing only a single field in model
@Tangaraj, if you mean that you one that a group can edit only one field of a model and cannot edit the other fields (note that the group still need to be able to edit write_uid and write_date), AFAIK, there is no straight-forward way. One possible solution is to use a function field as what I've described in the first option in my answer here. However, since your case is actually quite the opposite, you need to add the readonly attribute of ALL fields EXCEPT for the one that you want the group to edit.
Another option is to create a different form with all the fields set to readonly aside from one that the group can edit, then use this form in a new act_window and menu that this group can accessed. The other menu that accesses the same model has to be "protected" from this group as well by also assigning groups to those menu. Now, the next step is administrative, i.e. users that belong to one group cannot belong to the other.
In OpenERP V7.0, you can use "Field access rights" to protect your fields from being read or edited.
related question to read: https://www.odoo.com/forum/help-1/question/field-level-read-access-rights-missing-in-odoo-8-0-67530