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The Group pm

Generators: t1,t2, M
Relations: M2 = 0
Cell diagram: [Image]


Table: Six homomorphisms from pm
type P(k) = -1 wallpaper type of kernel group, with remarks
pm [Image] none pm, same as the extended group
pm' M p1
p'b1m [Image] t1 pm = {t12, t2, M}
p'bm [Image] t2 pm = {t1, t22, M}; new negating mirror
  M and t2 same as above, i(M) = M t2
p'bg [Image] t1 and M pg = {t12, t2, t1 M}; doubled cell
  t2 not a new type, interchange t1 and t2
c'm t1 and t2 cm = {t1 t2, t1 t2-1, M}; doubled cell
  M, t1 and t2 same as above, i(M) = M t2


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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