we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...

The codegree threshold ex 2 ( n , F ) $\operatorname{ex}_2(n, F)$ of a 3-graph $F$ is the minimum d = $d=d(n)$ such that every on $n$ vertices in which pair contained at least + 1 $d+1$ edges contains copy as subgraph. We study when K 4 − $F=K_4^-$ with 3 edges. Using flag algebra techniques, we prove if sufficiently large, then ⩽ . $$\begin{equation*} \hspace*{76pt}\operatorname{ex}_2(n, K_4^-...