https://www.jstage.jst.go.jp/article/tmj1911/17/0/17_0_88/_pdf
Page 90, third paragraph, where it says
"By continuing this process we arrive at a group $H_m$ containing the central of G and each of the operators $s_1, s_2, ... , s_m$ and involving only commutative involutions. If these operators generate $H_{m}'$ we represent $H_{m}'$ by $H_{m}$. If this is not the case we let $H_{m}$ represent the subgroup of index 2 under $H_{m}'$ generated by all its involutions."
I don't believe the notation has anything to do with commutator/derived subgroups and I couldn't find any explanation of it either on the paper itself or on the textbook he wrote unless it is related to whatever is going on in section 14 here https://archive.org/details/theoryapplicatio00milluoft/page/34 but that still doesn't help me make sense of what he means on the paper.