A note on the triple product property for subsets of finite groups
2011 ◽
Vol 14
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pp. 232-237
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AbstractThe triple product property (TPP) for subsets of a finite group was introduced by Henry Cohn and Christopher Umans in 2003 as a tool for the study of the complexity of matrix multiplication. This note records some consequences of the simple observation that if (S1,S2,S3) is a TPP triple in a finite group G, then so is (dS1a,dS2b,dS3c) for any a,b,c,d∈G.Let si:=∣Si∣ for 1≤i≤3. First we prove the inequality s1(s2+s3−1)≤∣G∣ and show some of its uses. Then we show (something a little more general than) that if G has an abelian subgroup of index v, then s1s2s3 ≤v2 ∣G∣.
2005 ◽
Vol 04
(02)
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pp. 187-194
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2016 ◽
Vol 15
(03)
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pp. 1650053
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1982 ◽
Vol 92
(1)
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pp. 55-64
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2019 ◽
Vol 18
(08)
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pp. 1950159
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1985 ◽
Vol 37
(3)
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pp. 442-451
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