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The Group cmm

Generators: d, Mx, R
Relations: d' = Mx d Mx-1, t1 = d'd-1, t2 = d'd,
R2 = e, Mx2 = e
Cell diagram: [Image]

Table: Six homomorphisms from cmm
type P(k) = -1 wallpaper type of kernel group, with remarks
cmm [Image] none cmm, same as the extended group
cmm' [Image] R cm = {t1, Mx}
  R and Mx same as above, i(M) = R Mx
cm'm' Mx p2 = {d, d', R}
p'cmm [Image] d pmm = {t1, t2, Mx, R}; cell doubled
p'cmg [Image] d and R pmg = {t1, t2, Mx, d R}; cell doubled
  d, R and Mx same as above, i(M) = R Mx
p'cgg d and Mx pgg = {d Mx (= L), R}; cell doubled

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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