Simple twisted group algebras of dimension p⁴ and their semi-centers

2014/12/08 by Ofir Schnabel, Schnabel, Ofir · 1 citation
Mathematics · #16S35 #20C25 #20E99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1412.2490

openalex publication_date 2014/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For simple twisted group algebra over a group G, if G^\shortmid is Hall subgroup of G then the semi-center is simple. Simple twisted groups 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 non-commutative and this bounds are strict.

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