The generator of second homotopy module of 〈x,y;xyx=yxy〉 and 〈a,b;a^2,b^3〉

2016 ◽  
Vol 11 ◽  
pp. 583-590
Author(s):  
Yanita ◽  
Dedi Mardianto
Keyword(s):  
Homotopy Module

SOME EXACT SEQUENCES FOR THE HOMOTOPY (BI-)MODULE OF A MONOID

2002 ◽  
Vol 12 (01n02) ◽  
pp. 247-284 ◽  
Author(s):  
YUJI KOBAYASHI ◽  
FRIEDRICH OTTO
Keyword(s):  
Finiteness Conditions ◽  
Type Formula ◽  
Homotopy Module ◽  
The Relationship ◽  
Finite Derivation Type ◽  
Finitely Presented ◽  
Exact Sequences ◽  
Homological Type

For finitely presented monoids the homological finiteness conditions left-[Formula: see text], left-[Formula: see text], right-[Formula: see text] and right-[Formula: see text], the homotopical finiteness conditions of having finite derivation type [Formula: see text] and of being of finite homological type [Formula: see text] are developed and the relationship between these notions is investigated in detail. In particular, a result of Pride [40] and Guba and Sapir [27] on the exactness of a sequence of bimodules for the homotopy module is proved in a completely different, purely combinatorial manner. This proof is then translated into a proof of the corresponding result for the left homotopy module, thus giving new insights into the relationship between the finiteness conditions considered.

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