There are interesting theorems about groups as union of proper subgroups. The first result in this subject is the theorem of Scorza(1926): "a groups if union of three proper subgroups if and only it has quotient $C_2\times C_2$." In 1959, Haber and Rosenfeld proved interesting theorems on the groups as union of subgroups. Then, in 1994, J. H. E. Cohn proved some interesting theorems about groups as union of few proper subgroups, and made conjectures.
While reading these three papers, which have large gaps in the publishing years, I couldn't find other initial references on "Groups as union of subgroups".
It will be a great pleasure, if one provides a list of references on the subject "Groups as union of proper subgroups", from 1926 to 1959 and from 1959 to 1994.
Especially, it is known that a non-cyclic $p$-group can not be union of $p$-proper subgroups, and if it is union of $p+1$ proper subgroups, then all the subgroups are maximal, and theire intersection has index $p^2$ in $G$. I would like to get original references for this theorem also.
Thanks in advance!!