Let $V$ be a $k$ -partite set means $V = V_1 \cup V_2 \cup \cdots \cup V_k $. Let $ G \le Sym(V_1) \times \cdots \times Sym(V_k)$ be a direct product group. Now consider the group action of $G$ on set $V$ (assume it is transitive on each $V_i$):
$$\pi : G \times V \mapsto V$$
Then each $V_i$ ha...
I am not sure how you can get blocks on which $G$ acts as either a symmetric or alternating group. I mean, what if you just have the cyclic group of order $p$ (for some prime $p$) acting in the obvious way on a set with $p$ elements?
$G \times \{B_1,B_2,\cdots B_k\} \mapsto \{B_1,B_2,\cdots B_k\} $, here $G$ is going to be symmetric or an alternating group ( $G$ is a direct product group )
Discussion between LLL and Tobias Kil…
Discussion between LLL and Tobias Kil…