- #1

karush

Gold Member

MHB

- 3,269

- 5

$\textit{ For the following groups,}$$(a)\quad \Bbb{Z}_6 \text{ the identity is } \color{red}{0}$

$(b)\quad |\Bbb{Z}_6|=\color{red}{6}$

$(c)\quad |0|=\color{red}{0}$

$(d)\quad |3| =\color{red}{|0,3|}$

$(e)\quad \text{the inverse of 2 is } \color{red}{4}$

$(f)\quad \text{the generator of this group is cyclic groups generated by } \color{red}{ 1}$

$(g)\quad \textit{Abelian/non-Abelian?} \quad \color{red}{Abelian}$

$(h)\quad Z_6 \text{ has $\color{red}{4 }$ subgroups.}$Sorta?

$(b)\quad |\Bbb{Z}_6|=\color{red}{6}$

$(c)\quad |0|=\color{red}{0}$

$(d)\quad |3| =\color{red}{|0,3|}$

$(e)\quad \text{the inverse of 2 is } \color{red}{4}$

$(f)\quad \text{the generator of this group is cyclic groups generated by } \color{red}{ 1}$

$(g)\quad \textit{Abelian/non-Abelian?} \quad \color{red}{Abelian}$

$(h)\quad Z_6 \text{ has $\color{red}{4 }$ subgroups.}$Sorta?

Last edited: