Does anybody know what the following means? It was never introduced in the lecture...
What is the meaning of $\mathbb{Z}^{n}$? And the meaning of $\#(G/2G)$ where $G$ is a additive group?
Thanks for all efforts.
Does anybody know what the following means? It was never introduced in the lecture...
What is the meaning of $\mathbb{Z}^{n}$? And the meaning of $\#(G/2G)$ where $G$ is a additive group?
Thanks for all efforts.
The expression $\mathbb{Z}^n$ denotes the collection of $n$-tuples of integers, i.e. $\mathbb{Z}^n=\underbrace{\mathbb{Z}\times\cdots\times\mathbb{Z}}_{n\text{ times}}=\{(a_1,\ldots,a_n)\mid a_i\in\mathbb{Z}\}$ It is a group under coordinate-wise addition; see product group.
The expression $\#(G/2G)$ denotes the cardinality (i.e. size) of the quotient group $G$ modulo the subgroup $2G$. The subgroup $2G$ is defined to be $2G=\{2g\mid g\in G\}$ where $2g=g+g$.