How to get values from IGrouping

foreach (var v in structure) 
{     
    var group = groups.Single(g => g.Key == v. ??? );
    v.ListOfSmth = group.ToList();
}

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First you need to select the desired group. Then you can use the ToList method of on the group. The IGrouping is a IEnumerable of the values.

Since IGrouping<TKey, TElement> implements IEnumerable<TElement>, you can use SelectMany to put all the IEnumerables back into one IEnumerable all together:

List<smth> list = new List<smth>();
IEnumerable<IGrouping<int, smth>> groups = list.GroupBy(x => x.id);
IEnumerable<smth> smths = groups.SelectMany(group => group);
List<smth> newList = smths.ToList();

Here's an example that builds/runs: https://dotnetfiddle.net/DyuaaP

Video commentary of this solution: https://youtu.be/6BsU1n1KTdo