I am referring to this proof I have a few questions:
- Is $\mathbb Z$ here, the centralizer of $\mathbb G$ ?
- How did they arrive at this conclusion?
The order of $\mathbb H$ is obviously $a_ia_2...a_h$
Thanks for your help Soham
Note, the relevant part of the proof for this question is that $G$ is a finite group with $h$ elements $g_1, g_2 \dots g_h$ having orders $a_1, a_2, \dots a_h$ respectively. We define a group $H$ of order $a_1a_2\dots a_h$ as follows:
$H=\bigoplus_{i=1}^h\mathbb Z/a_i\mathbb Z$
and proceed to use a homomorphism from $H$ to $G$ to prove Cauchy's theorem.