Формула максимально возможного ранга коммутантов конечных $p$-групп
О максимальном ранге коммутантов конечных p-групп
Keywords:
finite $p$-group generated by elements of orders $p^{k_1},\dots,p^{k_n}$, number of generators of commutator subgroup of a finite $p$-group, definition of a group by means of generators and defining relationsAbstract
The formula of maximal possible rank of commutator subgroups of finite $p$-groups
All groups in the abstract are finite. We define rank $d(G)$ of a $p$-group $G$
as the minimal number of generators of $G$.
In this paper, we obtain a compact formula for the strict upper bound of the ranks of commutator subgroups of
finite $p$-groups generated by elements of given orders. This bound was described in a recent article of the author.
But the corresponding formula was very complicated although containing some useful information. The new formula
is much more simple and clear.
Published
2023-08-03
Issue
Section
Mathematical logic, algebra and number theory
