A density theorem related to Dihedral groups
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
For a finite group $G$, let $\psi(G)$ denote the sum of element orders of $G$. If $\psi^{\prime\prime}(G)=\frac{\psi(G)}{|G|^2} $, we show here that the image of $\psi^{\prime\prime}$ on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\frac{1}{4}]$. We also derive some properties of $\psi^{\prime\prime}$ on the class of all dihedral groups whose order is twice a prime number.
Abstract
For a finite group $G$, let $\psi(G)$ denote the sum of element orders of $G$. If $\psi^{\prime\prime}(G)=\frac{\psi(G)}{|G|^2} $, we show here that the image of $\psi^{\prime\prime}$ on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\frac{1}{4}]$. We also derive some properties of $\psi^{\prime\prime}$ on the class of all dihedral groups whose order is twice a prime number.
참고문헌 (14)
- H. Amiri, "Sum of element orders on finite groups of the same order", J. Algebra Appl, 10(2), pp.187~190 (2011)[DOI]
- H. Amiri, "Sums of element orders in finite groups", Comm. Algebra, 37(9), pp.2978~2980 (2009)[DOI]
- T. M. Apostol, "Calculus. Vol. I" (1967), Blaisdell Publishing Co.
- M. Herzog, "An exact upper bound for sums of element orders in non-cyclic finite groups", J. Pure Appl. Algebra, 222(7), pp.1628~1642 (2018)[DOI]
- M. Herzog, "Sums of element orders in groups of order 2m with m odd", Comm. Algebra, 47(5), pp.2035~2048 (2019)[DOI]
- S. M. Jafarian Amiri, "Second maximum sum of element orders on finite groups", J. Pure Appl. Algebra, 218(3), pp.531~539 (2014)[DOI]
- S. M. Jafarian Amiri, "Characterization of p-groups by sum of the element orders", Publ. Math. Debrecen, 86(1-2), pp.31~37 (2015)[DOI]
- M. Jahani, "The minimum sum of element orders of finite groups", Int. J. Group Theory, 10(2), pp.55~60 (2021)
- M. -S. Lazorec, "A density result on the sum of element orders of a finite group", Arch. Math. (Basel), 114(6), pp.601~607 (2020)[DOI]
- Z. Nitecki, "Cantorvals and subsum sets of null sequences", Amer. Math. Monthly, 122(9), pp.862~870 (2015)[DOI]
- R. Shen, "On groups with the second largest value of the sum of element orders", Comm. Algebra, 43(6), pp.2618~2631 (2015)[DOI]
- W. A. Sutherland, "Introduction to Metric and Topological Spaces" (2009), Oxford Univ. Press
- M. Tarnauceanu, "Detecting structural properties of finite groups by the sum of element orders", Israel J. Math, 238(2), pp.629~637 (2020)[DOI]
- M. Tarnauceanu, "On the sum of element orders of finite abelian groups", An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N. S. ), 60(1), pp.1~7 (2014)[DOI]