025-2011

MO640 - Multiple-choice question

Among the statements below, choose the INCORRECT one.

a) Given a permutation α, its inverse α^-1 is obtained by inverting the order of elements in each cycle of the cycle decomposition of α.
b) Let α = (a b) and β be any permutation. If a and b are in the same cycle in the cycle decomposition of β, then this cycle will be partitioned into two in the cycle decomposition of αβ.
c) Let α = (a b) and β be any permutation. If a and b are in separate cycles in the cycle decomposition of β, these cycles will turn into a single cycle in the cycle decomposition of αβ.
d) Let α = (a b c) and β be a permutation in which a, b, and c are distributed over two distinct cycles.  The total number of cycles in αβ will be less than the total number of cycles in β.
e) None of the above.

Translated by: Raphael Cristofaro
Original idea by: Kaio Karam