If you want members in a group to be able to read the memberships of the group (and view that it exists), then you can put a rule on a folder so that new groups will have a privilege assigned so that the group itself is assigned to be a READer of the group
grouperSession = GrouperSession.startRootSession();
folder = StemFinder.findByName(grouperSession, "testFolder");
AttributeAssign attributeAssign = folder.getAttributeDelegate().addAttribute(RuleUtils.ruleAttributeDefName()).getAttributeAssign();
AttributeValueDelegate attributeValueDelegate = attributeAssign.getAttributeValueDelegate();
attributeValueDelegate.assignValue(RuleUtils.ruleActAsSubjectSourceIdName(), "g:isa");
attributeValueDelegate.assignValue(RuleUtils.ruleActAsSubjectIdName(), "GrouperSystem");
attributeValueDelegate.assignValue(RuleUtils.ruleCheckTypeName(), RuleCheckType.groupCreate.name());
attributeValueDelegate.assignValue(RuleUtils.ruleCheckStemScopeName(), Stem.Scope.SUB.name());
attributeValueDelegate.assignValue(RuleUtils.ruleThenElName(),"${ruleElUtils.assignGroupPrivilege(groupId, 'g:gsa', groupId, null, 'read')}");