To remove the space between the comma and the train_index array:

This results in:

TRAIN:  Index: [2 3], Group: [2 2]

I'm thinking this information is better in the LeaveOneGroupOut section. As a reader learning about just GroupKFold, I think this is too much information. But if I was reading about LeaveOneGroupOut, it is nice to know that LeaveOneGroupOut is a special case of GroupKFold.

Nit: Using "with" here is more consistent with the first part of the sentence which says "with n_groups=1"

What about including information on the fold to make it a little more clear what is happening?

Fold 1:
    train_index=[2 3], train_group=[2 2]
    test_index=[0 1 4 5], test_group=[0 0 3 3]
Fold 2:
    train_index=[0 1 4 5],  train_group=[0 0 3 3]
    test_index=[2 3], test_group=[2 2]

I thought about this but couldn't think of a way to do it neatly, I got (first line is a bit too long):

    >>> for i, (train_index, test_index) in enumerate(group_kfold.split(X, y, groups)):
    ...     train_group, test_group = groups[train_index], groups[test_index]
    ...     print(f"Fold {i}")
    ...     print(f"\tTRAIN:\tIndex: {train_index}, Group: {train_group}")
    ...     print(f"\tTEST:\tIndex: {test_index}, Group: {test_group}")

WDYT?

I personally don't mind this, and I don't think you can make that first line shorter without changing the variable names or doing something non-Pythonic. Another way would be the following, which produces what I had above – it makes the print() statements easier to follow, but the first line is the same:

    >>> for i, (train_index, test_index) in enumerate(group_kfold.split(X, y, groups)):
    ...     train_group, test_group = groups[train_index], groups[test_index]
    ...     print(f"Fold {i + 1}")
    ...     print(f"\t{train_index=}, {train_group=}")
    ...     print(f"\t{test_index=}, {test_group=}")

Thanks, happy to amend but would like to get some other opinions (maybe @thomasjpfan?) just because I would like to update all other similar example sections for other classes in _split.py (e.g., GroupKFold) to the same format.

Given what we decide here will influence other examples, I prefer to split this PR into two. This PR can only do what the title states and update doc/modules/cross_validation.rst.

Then you can open a new PR for this docstring's example where we can agree on a formatting. As for my opinion, I like:

for i, (train_index, test_index) in enumerate(group_kfold.split(X, y, groups)):
    print(f"Fold {i}:")
    print(f"  Train: index={train_index}, group={groups[train_index]}")
    print(f"  Test:  index={test_index}, group={groups[test_index]}")

which turns into:

Fold 0:
  Train: index=[2 3], group=[2 2]
  Test:  index=[0 1 4 5], group=[0 0 3 3]
Fold 1:
  Train: index=[0 1 4 5], group=[0 0 3 3]
  Test:  index=[2 3], group=[2 2]

Edit: Corrected with group=

As suggested by @stefmolin, I like having the fold number in, but I find https://github.com/scikit-learn/scikit-learn/pull/24104/files#r964290370 harder to parse:

Fold 1
	train_index=array([2, 3]), train_group=array([2, 2])
	test_index=array([0, 1, 4, 5]), test_group=array([0, 0, 3, 3])
Fold 2
	train_index=array([0, 1, 4, 5]), train_group=array([0, 0, 3, 3])
	test_index=array([2, 3]), test_group=array([2, 2])

That also LGTM. Should it be group= to match index=?

Yes it should be group=.

Wording tweak to avoid possible confusion with the parameter n_groups.