Equivalence of -algebras for abelian

Author:
Alexandre Turull

Journal:
Proc. Amer. Math. Soc. **123** (1995), 1655-1660

MSC:
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-1995-1249894-9

MathSciNet review:
1249894

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Abstract: We describe the equivalence classes of central simple *G*-algebras over an infinite field *F* for *G* a finite abelian group, provided the following holds. For each prime *p* for which the field *F* has primitive *p*th roots, the Sylow *p*-subgroup of *G* is either cyclic or elementary abelian.

**[1]**T. Y. Lam,*The algebraic theory of quadratic forms*, Benjamin, Reading, MA, 1973. MR**0396410 (53:277)****[2]**A. Turull,*The Schur index of projective characters of symmetric and alternating groups*, Ann. of Math. (2)**135**(1992), 91-124. MR**1147958 (93c:20026)****[3]**-,*Clifford theory with Schur indices*, J. Algebra (to appear). MR**1302862 (95h:20012)****[4]**-,*Some invariants for equivalent G-algebras*, J. Pure Appl. Algebra (to appear). MR**1319970 (96a:16035)****[5]**-,*Equivalence of G-algebras with complemented centroid*, Comm. Algebra**22**(1994), 5037-5078. MR**1285725 (95j:16023)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1249894-9

Keywords:
Brauer group,
*G*-algebra,
finite groups,
representations

Article copyright:
© Copyright 1995
American Mathematical Society