For an odd prime $p$, we prove that a finite powerful $p$-group having rank two Frattini quotient has nonzero essential cohomology. We also provide some examples and applications.
Cohomology of groups, essential cohomology, powerful $p$-groups
AKSU, FATMA ALTUNBULAK
"On essential cohomology of powerful $p$-groups,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 35.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/35