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On 05/11/95 at 17:57:14 mreid@ptc.com said:

jerry asks about P-symmetric positions. coincidentally, i happened

to investigate these a few weeks back, and here's what i found:

(i calculated by hand, so i'd be grateful for any confirmation.)there are 128 P-symmetric positions, 4 of which are M-symmetric.

I can confirm your count. These positions are called X class positions

in Dan's taxonomy. That is, there are 124 positions Y unique up to

M-conjugancy for which Symm(Y)=X1 or Symm(Y)=X2 or Symm(Y)=X3, where

X1, X2, and X3 are the three conjugate subgroups of M in Dan's

taxonomy of subgroups which contain sixteen elements. Hence, we

describe the 124 positions as being class X positions. The 4

M-symmetric positions are also X-symmetric, but we don't count them

as class X.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU