MathDB

The house SEAT recommends to the users, for the correct conservation of the wheels, periodic replacements of the same in the form

R \to 3 \to 2 \to 1 \to 4 \to R

, according to the numbering of the figure. Calling

G

to this change of wheels,

G^2 = GG

to making this change twice, and so on for the other powers of

G

, a) Show that the set of these powers forms a group, and study it. b) Each puncture of one of the wheels is also equivalent to a substitution in which said wheel is replaced by the spare one

(R)

and, once repaired, it comes to occupy the place of this obtained

G

as a product of prick transformations. Do they form a group? https://cdn.artofproblemsolving.com/attachments/4/a/712fede88321c67753417fda828a08ba528b4f.png

8

Problems(1)