Fields in physics and fields in group theory, are they related?

I just though of this and though "it's abstract math meeting physics, so probably not". After looking up fields in several abstract algebra books I thought that maybe fields in physics were called as such in physics because they share something with the mathematical structure of fields in group theory. I'm highly interested in both physics and abstract mathematics but at the moment don't have time to look this up myself, so I ask this: Do fields in group theory share anything with fields in physics? (Excluding the fact that one is abstract and the other is a physical quantity)

Please I'd appreciate answers that actually look into this instead of just saying "what does abstract math have to do with physics". I mostly want to prove to my self that the naming is just a coincidence, but I just can't help wondering since group symmetries are used in a lot of aspects of upper level physics.