2. Let Y=<u,v/u^4=v^3=1, uv=v^2u^2> Y here is a group show
b) v commutes with u^3
c) v commutes with u
e)u=1, deduce that v=1 and conclude that Y=1
If 1,x,x^2,...,x^(n-1) is not distinct, then we can find some 0<=i<j<=n-1, such that x^i = x^j. Then ...
Groups, Order and Commutativity are investigated.
Abstract algebraic operations
Show that the operation * on the real number is defined by a*b = ab + a^2 is neither associative nor commutative.
Show that * on R is defined by a*b = a+b+2 is both associative and commutative
* The movements of a robot are restricted to no change (N), turn left (L), turn right (R), and turn about (A). Construct a Cayley Table and show that this set of movements forms a group.
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