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The Group pmg

Generators: t1, Lv, A
Relations: A2 = 0, Lv2 = t2, Lv A = Rc
Cell diagram: [Image]

Table: Six homomorphisms from pmg
type P(k) = -1 wallpaper type of kernel group, with remarks
pmg [Image] none pmg, same as the extended group
p'bmg [Image] t1 pmg = {t12, Lv, A}
  t1 and Lv same as above, i(Lv) = Lv t1
pmg' [Image] Lv pm = {t1, Lv2, A}; R negative
pm'g [Image] A pg = {t1, Lv}; R negative
p'bgg t1 and A pgg = {t12, Lv, t1 A}; doubled cell
  t1, Lv and A same as above, i(Lv) = Lv t1
pm'g' [Image] Lv and A p2 = {t1, Lv2, Lv A}; R positive

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Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 08 Jul 1998 --- Last modified: 18 Aug 1998 23:59:59
Comments to: CVM@maa.org