According to information I've read it could be caused by iron deficiency.
The medical name is onychoschizia!
Also possible thyroid problem?
Sqad might be able to assist - in his inimitable way :-)
She could use a supplement if she doesn't eat much milk and dairy. It might be worth encouraging her as her bones and teeth need it too and the nails might be only the start of it if she's lacking.
She won't take tablets. She has to take regular medication, and makes a terrible fuss over it. She doesn't drink milk either, other than in tea - but she drinks plenty of that. She'll eat the odd piece of cheese, or a yoghurt sometimes, but that's about it. I'm not sure if that would be enough - or perhaps, as yoga says, an iron deficiency could be the problem. Thinking about it, she doesn't eat much that contains that either.