Abstract
Let g_1H_1,ldots ,g_nH_n be cosets of subgroups H_1,ldots ,H_n of a finite group G such that g_1H_1cup ldots cup g_nH_nne G. We prove that |g_1H_1cup ldots cup g_nH_n|le gamma _n|G| where gamma _n<1 is a constant depending only on n. In special cases, we show that gamma _n=(2^n-1)/2^n is the best possible constant with this property and we conjecture that this is generally true.
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