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ON THE SUBSTITUTION GROUPS FOR TWO, THREE, FOUR, 
FIVE, SIX, SEVEN, AND EIGHT LETTERS. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xxv. (1891), 
pp. 71—88, 137—155.] 
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The substitution groups for two, three, four, and five letters were obtained by 
Serret: those for six, seven and eight letters have recently been obtained by 
Mr Askwith. I wish to reproduce these results in a condensed form. 
The following table shows for the several cases respectively, the orders of the 
several groups, and for any order the number of distinct groups. As regards the 
case of eight letters, the numbers mentioned do not exactly agree with Mr Askwith: 
he gives a few non-existent groups, and omits some which I have supplied (see 
post, the list of the groups for eight letters); and it is possible that there are 
other omissions: the several numbers in the column and the sum total of 155 are 
given subject to correction.