It is possible to calculate something like avg(a) + avg(b) group by c

I don't know how to make my explanation, for example in sql

SELECT c,avg(a) + avg(b) as count FROM name group by c;

It is possible to write using in elasticsearch? Thanks!

I do think so (my SQL skills are very rusty after years of Elasticsearch), but a terms aggregation with two nested avg aggregations might be what you are searching for.