Dialog system of symbolic calculations in burnside groups

A programming system designed for use in group theory is described. The $ALCOS/G-B$ dialog system automates the very tedious analytic calculations that arise in the study of various Burnside groups. A problem that requires development of a dialog system and the procedures underlying ALCOS/G-B are described. The means given to the user of the system are indicated. The use of $ALCOS/G-B$ to calculate the nilpotency class of one of the Burnside groups with two generators of exponent 8 whose commutator has nilpotency class 3 is described as an example. It is found that the nilpotency class of this group does not exceed 24.