The stable behavior of the augmentation quotients of some groups of order p4, I

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概要

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• We list the stable structure of these six groups below.(1) G1=Zp׋x, y, z|xp=yp=zp=[x, z]=[y, z]=1, [x, y]=z›, n0=3p-2, π=2 Q3p-2(G1)=Zp(1/2)(p+1)(p2+p+1), Q3p-1(G1)=Zp(1/2)(p+1)(p2+p+1)+1(2) G2=‹u, x, y|up=xp=yp2=[u, y]=[x, y]=1, [u, x]=yp›, n0=3p-2, π=1, Q3p-2(G2)=Zp(2p2+p+1).(3) G3=Zp׋x, y|xp=yp2=1, [x, y]=yp›, n0=3p-2, π=1, Q3p-2(G3)=Zp(2p2+p+1).(4) G4=Zp(2)×Zp2 n0=3p-2, π=1, Q3p-2(G4)=Zp2×Zp(2p2+p-1).(5) G5=‹u, x, y|up=xp=yp2=[u, x]=[u, yp]=1, [u, y]=x, [x, y]=yp›, n0=4p-3, π=2, Q4p-3(G5)=Zp(1/2)(3p2+1)+p, Q4p-2(G5)=Zp(3/2)(p2+1)+p(6) G6=‹u, x, y|up=xp=yp2=[u, x]=[x, y]=1, [u, y]=x›, n0=4p-3, π=2, Q4p-3(G6)=Zp2×Zp(3/2)(p2-1)+p, Q4p-2(G6)=Zp2×Zp(1/2)(3p2-1)+p.

• 社団法人 日本数学会の論文

著者

• TAHARA Ken-ichi

  Department of Animal Physiology, Graduate School of Bioagricultural Sciences, Nagoya University

• TAHARA Ken-Ichi

  DEPARTMENT OF MATHEMATICS AICHI UNIVERSITY OF EDUCATION IGAYA-CHO

• HORIBE Kazunori

  DEPARTMENT OF MATHEMATICS AICHI UNIVERSITY OF EDUCATION IGAYA-CHO

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