Simple Twisted Group Algebras of Dimension p4 and their Semi-Centers |
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Authors: | Ofir Schnabel |
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Institution: | 1. Institute of Algebra and Number Theory, University of Stuttgart, Stuttgart, Germanyos2519@yahoo.com |
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Abstract: | For a simple twisted group algebra over a group G, if G∣ is Hall subgroup of G, then the semi-center is simple. Simple twisted group algebras correspond to groups of central type. We classify all groups of central type of order p4 where p is prime and use this to show that for odd primes p there exists a unique group G of order p4, such that there exists simple twisted group algebra over G with a commutative semi-center. Moreover, if 1 < |G| <64, then the semi-center of simple twisted group algebras over G is noncommutative and this bounds are strict. |
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Keywords: | Groups of central type Semi center Twisted group rings |
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