There is an option in the group listings, for the owner to choose whether or not a group is shown in the profile. There are many cases where allowing people to hide their groups would be a bad thing. For example, "I am for a free second life". Having that group in your profile is a political statement, and to hide it would render it pointless. I can see why Jazhara made it visible, and I do not think this should be changed.

If you don't like the admin's choice of visibility, you're free to leave a group.

There are probably more people who abuse the current situation than would abuse the situation where anyone could hide groups from their profile.
Right now, there are several types of groups whose creators may choose to show in member profiles, to gain an advantage from members :

• groups run by companies, for product updates/support/etc - who want free advertising
• groups run as "friends lists" - by people who want ego-building
• special interest groups which seek to promote their cause at the expense of members' privacy
  IMHO, the current system is more likely to lead to group owners taking advantage of their members, than the proposed change is to lead group members to take advantage of their group owners.

=== This could be done in a way OK for Jazhara's group ===

If the Jazhara case is a serious problem, why not add a group role permission "can hide membership from profile"? That would allow groups for whom publicity is very important to continue as they are now. So long as that power was given to everybody by default, it would still result in a big privacy gain for most people.

However, there are also other reasons why it is a good idea.

One such reason is preventing confusing or misleading situations.

Example confusing situation :
1) I own a string of islands.
2) Due to problems with griefers, I deploy SLBanLink (http://www.slbanlink.com) devices on my sims, in order to detect and eject griefers before they can cause problems. It is fairly important that I do this, as there are high-traffic clubs on my sims, and as a good sim owner, I feel obligated to help protect them, especially when they are the targets of griefers with sim-crashing weapons.
3) To make sure BanLink works, I have to make sure there is a BanLink orb on every single parcel, and further, that the orb is deeded to the same group that the parcel is.
4) Some tenants take long 'holidays' during which I cannot contact them. Plus, I don't really want to hassle my customers each and every time I either want to install a new device, or replace an existing one (e.g. due to improvements in the scripts). I have to make sure there is a working, up-to-date device on every parcel, for a single parcel left unprotected and build-enabled can be used to crash a sim.
5) Therefore, I have to be in pretty much every group that owns land on my islands. And not just in the 'everyone' role, either. Usually I get assigned to the 'Owners' role or some other high-ranking role that has 'can deed objects to group' permissions, because I need that permission to deed objects to the group on the group-owned parcels.
6) Unfortunately, some of the groups that own land on my islands would paint a very misleading picture of me if they showed in my profile. Some of these groups are innocent but cause minor misunderstandings (e.g. groups like "Dutch Residents", which would incorrectly imply that I'm Dutch). Some cause more important misunderstandings (e.g. groups like "Friends of ____" or "Anti-____", which would say something untrue about my social relationships). Some misunderstandings can be quite serious. For example, even having a group like "Transsexual Masters and Slaves" in your profile can cause people to react to you very differently. People never bring it up with you, either. They just treat you differently and leave you to wonder why.
7) Many of these groups are for clubs and other public areas, and as such, the group owner wants them to show in peoples' profiles for advertising reasons. Even when some roles are hidden, the fact that I usually get allocated a high-up role to do the BanLink orb deeding means I'm likely to show up in the members list.
8) Further, I quite often get people (usually newbies wanting a house for them and their friends) who are confused about the group tools. Often, this means I end up founding the groups for them, as this is more convenient for us both, especially when they pay me via PayPal and don't maintain any L$ balance. Founding the group means I have no chance of staying hidden in the group members list. Even when the groups are private, the list of owners can always be pulled up by anyone using the about land tools on a parcel owned by the group.
9) So, the end result is that I have to join a lot of groups which have nothing to do with me, but I need to be in so I can provide services to my customers, who happen to own the groups. Most of the groups are entirely innocent but some are not, and it is these few non-innocent ones which sometimes cause misunderstandings if I have them listed in my profile. Even if the groups are invisible the potential for misunderstanding still persists.

There are some people like myself who have to be in certain groups for business reasons, but don't want those groups showing in our profiles because they'd create all sorts of misunderstandings if they did.
I'd spend a lot of time explaining that I'm not Dutch, not the best buddy of foo, not anti-foo, not staff at club foo, not a transsexual dragon that likes vore and people dressed up in foo outfits, not interested in foo-surfing, not campaigning to elect Mr. Foo, not in Foo's Family and Friends, and most certainly not partial to a tall order of foo with iced tea.

I still think the privacy of people who are really participants in such groups is a better reason than this "confusion prevention" reason for implementing the group privacy feature.

However, I'm still throwing this out there as an additional reason that this group privacy thing would be a good idea.

Personally, I have alts to hold group memberships for groups which own land on my sims. I have to. There are so many groups that there is no way in hell I'd ever fit them on my main! Plus, it saves me from people asking endless questions related to the finer points of foo.
Most people, however, don't have dedicated alts to hold all their group memberships.
Most people, if they really have to be in a group they don't want showing in their profile, are stuck with it, because there's not much they can do on their main, and shifting it to an alt does not occur to them.

I think this proposal would be a good idea, both on privacy grounds, and on the grounds that it would prevent misunderstandings.

I agree that security officers (such as bouncers at clubs) do sometimes look at group memberships in an effort to identify potential troublemakers, and during some types of griefing attacks (e.g. particle spam) where the identity of the griefer is not obvious.

Nevertheless I still feel that the privacy gains for ordinary decent people make this feature worth implementing.

Griefers that are members of organized griefing gangs usually either use invisible groups or no groups at all, to prevent residents and Lindens respectively from identifying them.

Griefers which aren't members of organized griefing gangs might be members of a few groups of ill-repute, but usually, they don't know that they are being profiled by their group memberships.

Therefore, the security advantage of not allowing group members to hide their membership of the group from the public is a small one. It helps only in that it allows non-Lindens to better identify few griefers who do use groups and do have them public but would have set their personal membership of them to hidden were they aware of it. That's a pretty narrow case.

On the other hand, implementing this feature would give an additional level of privacy to every SL resident.

It seems pretty clear to me that a major privacy gain for all SL residents clearly outweighs a minor loss in terms of our ability to find out more about other avatars' group memberships.

So, I take your point. Yes implementing this feature might slightly reduce security officers' ability to profile people. This is annoying, but I think the privacy gains for all SL residents are worth it.