On the sum of two sets in a group
Sums C = A + B of two finite sets in a (generally non-abelian) group are considered. The following two theorems are proved. 1. ∣C∣ ≥ ∣A∣ + 1 2 ∣B∣ unless C + (− B + B) = C; 2. There is a subset S of C and a subgroup H such that ∣ S∣ ≥ ∣ A∣ + ∣ B∣ − ∣ H∣, and either H + S = S or S + H = S....
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| Published in | Journal of number theory Vol. 18; no. 1; pp. 110 - 120 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
1984
|
| Online Access | Get full text |
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| Summary: | Sums
C =
A +
B of two finite sets in a (generally non-abelian) group are considered. The following two theorems are proved. 1.
∣C∣ ≥ ∣A∣ +
1
2
∣B∣
unless
C + (−
B +
B) =
C; 2. There is a subset
S of
C and a subgroup
H such that ∣
S∣ ≥ ∣
A∣ + ∣
B∣ − ∣
H∣, and either
H +
S =
S or
S +
H =
S. |
|---|---|
| ISSN: | 0022-314X 1096-1658 |
| DOI: | 10.1016/0022-314X(84)90047-7 |