The Cauchy-Davenport Theorem for Finite Groups

Details The Cauchy-Davenport Theorem for Finite Groups The Cauchy-Davenport Theorem for Finite Groups

2012-02-08

arxiv.org/abs/1202.1816v1

Mathematics

Combinatorics

11 pages with references

Scientific paper

The Cauchy-Davenport theorem states that for any two nonempty subsets A and B
of Z/pZ we have |A+B| >= min{p,|A|+|B|-1}, where A+B:={a+b (mod p) | a in A, b
in B}. We generalize this result from Z/pZ to arbitrary finite (including
non-abelian) groups. This result from early in 2006 is independent of Gyula
Karolyi's 2005 result.

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