TY - JOUR

T1 - Quivers of groups with normal p-subgroups

AU - Schaps, Mary

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033245498&partnerID=8YFLogxK

U2 - 10.1080/00927879908826561

DO - 10.1080/00927879908826561

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AN - SCOPUS:0033245498

SN - 0092-7872

VL - 27

SP - 2231

EP - 2242

JO - Communications in Algebra

JF - Communications in Algebra

IS - 5

ER -