## Twisted product of cocycles and factorization of semi-regular relative difference sets.(English)Zbl 1148.05015

Summary: We introduce what we call twisted Kronecker products of cocycles of finite groups and show that the twisted Kronecker product of two cocycles is a Hadamard cocycle if and only if the two cocycles themselves are Hadamard cocycles. This enables us to generalize some known results concerning products and factorizations of central semi-regular relative difference sets.

### MSC:

 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
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### References:

 [1] Brown, Cohomology of groups (1982) [2] Chen, Relative difference sets fixed by inversion (III)-Cocycle theoretical approach, Discrete Math 308 pp 2764– (2008) · Zbl 1159.05009 [3] Chen, Constructions of partial difference sets and relative difference sets using Galois rings. II, J Combin Theory Ser A 76 pp 179– (1996) · Zbl 0859.05021 [4] Davis, A note on products of relative difference sets, Des Codes Cryptogr 1 pp 117– (1991) · Zbl 0754.05014 [5] Davis, Construction of relative difference sets in p-groups, Discrete Math 103 pp 7– (1992) · Zbl 0777.05023 [6] Galati, A group extension approach to relative difference sets, J Combin Des 12 pp 279– (2004) · Zbl 1045.05021 [7] Galati, Relative difference sets in semidirect products with an amalgamated subgroup, J Combin Des 13 pp 211– (2005) · Zbl 1067.05013 [8] Liu, Relative difference sets fixed by inversion (II)-Character theoretical approach, J Combin Theory Ser A 111 pp 175– (2005) · Zbl 1070.05016 [9] Perera, Cocyclic generalised Hadamard matrices and central relative difference sets, Des Codes and Cryptogr 15 pp 187– (1998) · Zbl 0919.05007 [10] Perera, Factorization of semiregular relative difference sets, Australas J Combin 22 pp 141– (2000) · Zbl 0972.05011 [11] Pott, Finite geometry and character theory, Lecture Notes in Mathematics 1601 (1995) · Zbl 0818.05001 [12] Pott, Groups, difference sets and the monster pp 195– (1996)
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