[math] \newcommand{\mathds}{\mathbb}[/math]

Prove that when lifting the uniformity assumption, the groups

[[math]] \xymatrix@R=50pt@C=50pt{ B_N\ar[r]&B_N'\ar[r]&O_N\\ S_N\ar[u]\ar[r]&S_N'\ar[u]\ar[r]&H_N\ar[u]} [[/math]]

with the convention [math]G_N'=G_N\times\mathbb Z_2[/math], are the only easy real groups.