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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