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Post Closed as "off topic" by Fernando Muro, Peter McNamara, Andres Caicedo, Theo Johnson-Freyd, Mark Sapir
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Is there formula name and proof for this theorem ?The formula answers: how many tuples $(\sigma_1,\sigma_2,...,\sigma_n)$ of elements of a given group G such that (1) $\sigma_i\in C_i$ , where $C_i$ stands for conjugacy class. (2) $\sigma_1\sigma_2...\sigma_n= id$ I want to know the name and exact content of this formula. Also , is there any connection between this formula and Burnside counting theorem (orbit-counting theorem)? I also want of a proof of the formula using idompotent (perhaps) and other related theorems. Thanks in advance.
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