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Characters of finite quasigroups. II: Induced characters. (English) Zbl 0599.20110

In part I [ibid. 5, 43-50 (1984; Zbl 0537.20042)] the authors introduced the elements of a theory of characters for finite non-empty quasigroups, generalizing the characters of finite groups. In the present paper, the development of this theory is continued by showing how characters of a subquasigroup may be induced up to characters of a containing quasigroup. The Frobenius reciprocity theorem and an analogue of Artin’s theorem for these characters are proved. Character rings of quasigroups are also examined.
Reviewer: C.Pereira da Silva

MSC:

20N05 Loops, quasigroups
20C99 Representation theory of groups

Citations:

Zbl 0537.20042
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References:

[1] Johnson, K.W.; Smith, J.D.H., Characters of finite quasigroups, Europ. J. combinatorics, 5, 43-50, (1984) · Zbl 0537.20042
[2] Serre, J.-P., (tr. L. L. Scott), linear representations of finite groups, Springer graduate texts in mathematics no. 42, (1977), Springer-Verlag New York
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