How do you get the rows that contain the max value for each grouped set?

I’ve seen some overly-complicated variations on this question, and none with a good answer. I’ve tried to put together the simplest possible example:

Given a table like that below, with person, group, and age columns, how would you get the oldest person in each group? (A tie within a group should give the first alphabetical result)

Person | Group | Age
---
Bob  | 1     | 32  
Jill | 1     | 34  
Shawn| 1     | 42  
Jake | 2     | 29  
Paul | 2     | 36  
Laura| 2     | 39  

Desired result set:

Shawn | 1     | 42    
Laura | 2     | 39  

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