Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 26, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Gyula Károlyi (Eötvös Lorand University)

Set addition in noncommutative groups

According to a classical result due to Cauchy and Davenport, if A and B are sets of congruence classes modulo a prime p, then at least |A|+|B|-1 different classes are represented by the Minkowski sum A+B (unless this number already exceeds the prime p). It is also known that, apart from some trivial or pathological cases, equality occurs only if A and B represent arithmetic progressions of the same difference.

Generalizations of these theorems to commutative groups in general are also widely known. In this talk I will present a natural counterpart of these results for the nonabelian case. The combinatorial proofs depend on the structure of group extensions.

I plan this talk to be pretty self-contained, so even if you forgot most of you may have learnt about groups, you will be able to follow it.

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