Cyclic Groups -- Abstract Algebra 7

[@ethanlipson1637]

Gonna start saying \mathbb instead of boldface

[@aashsyed1277]

What is mathbb?

[@aashsyed1277]

What is mathbb?

[@coreymonsta7505]

@@aashsyed1277 that’s a command in latex to make a letter look fancy, and like the way sets are usually written. So instead of Z, Q, F, D, C etc you say \mathbb{letter} to make it look that way

[@coreymonsta7505]

@@aashsyed1277 there’s also mathcal which is used sometimes as well. Diff style

[@fbkintanar]

@@aashsyed1277 it iabbreviates "math blackboard bold," I think. It is supposed to correspond to the font that math teachers informally write on the blackboard with an extra vertical line to indicate it is a different typeface from the usual letters.

[@grigoriefimovitchrasputin5442]

Can we use Lagrange's theorem to solve question 3?

[@aashsyed1277]

well lagranges theorem is not told at this point so technically no.

[@fahim1943]

Have you figured how to do it without Lagrange s Theorem?

[@themibo899]

@@fahim1943 it's simple, you know g^20 != e so g^10 must also, same reasoning applied to g^8 implies g^4,2 != e hence, since the order of an element divides the order of G (40 in this case), you are left with the g^40=e hence G=

[@SilverlightLantern]

!!Spoiler alert!! Oof apparently Z6x Z3 has 10 cyclic subgroups? :S