Quivers of groups with normal p-subgroups

Mary Schaps

Research output: Contribution to journalArticlepeer-review


Let K be a sufficiently large field of characteristic p. We determine the quiver of a semidirect product H = P ⋊ H̄ of a finite p-group by a finite group H̄, as the join of the quiver of H̄ and the McKay graph D(H̄, R̄′) of the conjugation representation R̄′ of H̄ on Rad(KP)/(Rad KP ∩ Rad2 (KH)). More generally, whenever P ⊴ H and H̄ → H/P, we show that the quiver QKH of H is a subgraph of the above join, and give a necessary and sufficient condition on the radicals for the quiver of H to exactly equal the join QKH̄ v D(H̄, R̄′). Finally, we identify the "transgressing" arrows of the McKay graph, those which do not appear in the quiver of H, with basis elements in the kernel of the transgression map.

Original languageEnglish
Pages (from-to)2231-2242
Number of pages12
JournalCommunications in Algebra
Issue number5
StatePublished - 1999


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