## Characters of finite quasigroups. III: Quotients and fusion.(English)Zbl 0667.20053

[Part II cf. ibid. 7, 131-137 (1986; Zbl 0599.20110).]
This paper examines two topics which do not extend directly from group- theoretical concepts, since they are respectively trivial or inapplicable in group theory. The first topic concerns the question of how characters of a homomorphic image lift to characters of the preimage. The second topic concerns sets Q carrying two quasigroup structures $$(Q,+)$$ and (Q,.), such that the multiplication group $$Mlt(Q,+)$$ of $$(Q,+)$$ is a subgroup of the multiplication group $$G=Mlt(Q,.)$$ of (Q,.). In part 3 of the paper, the Fusion Theorem shows how the character theory of (Q,.) is determined by the character theory of $$(Q,+)$$ and the way that (Q,.) “fuses” the conjugacy classes and characters of $$(Q,+)$$. Many results of this paper generalize readily to the case of a permutation group G and its subgroup H acting on a set Q, in such a way that the centralizer ring V(H,Q) of H on Q is commutative.
Reviewer: C.Pereira da Silva

### MSC:

 20N05 Loops, quasigroups 20C99 Representation theory of groups

Zbl 0599.20110
Full Text:

### References:

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