Question

Let C_10 denoted by {1,a,a^2,a^3,a^4,a^5,a^6,a^7,a^8,a^9}
C_5 x C_2 is denoted by {1,r,r^2,r^3,r^4,f,fr,fr^2,fr^3,fr^4}
C_10 is described by a^10=1
C_5 xC_2 is described by r^5 =1; f^2=1; rf = fr
Prove or disprove C_10 isomorphic with C_5 x C_2
Please, help

Answer 1

youll have to unpack the notation

Answer 2

why? that is what I have from the original problem

Answer 3

does C represent a cycle?

Answer 4

yap

Answer 5

the elements of C5 are apparently r^0 to r^4; what are the elements of C2? i see an f^1 but no f^0

Answer 6

C_5 x C_2 is a Q graph

Answer 7

Q is in a hypercube?

Answer 8

ahhh

Answer 9

both C_5 and C_2 have the same direction, f is back and forth

Answer 10

a cycle is a closed path (doesnt repeat edges or nodes) right?