Communications in Algebra, vol.52, no.2, pp.473-478, 2024 (SCI-Expanded)
Let p be a prime and P be a finite p-group. We define a new characteristic subgroup (Formula presented.) of P and show that (Formula presented.) is a critical subgroup of P. Secondly, we define several new characteristic subgroups (Formula presented.), (Formula presented.) for each positive integer i and show that they enjoy some interesting and new properties similar to the those of critical subgroups. Lastly, for a solvable group G, we define a new characteristic subgroup (Formula presented.), which satisfies the analogue of Thompson’s result for solvable groups.