Browsing by Author "Gorentas, Necat"

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Autg Tarafından Belirlenen Merkezleyen Yakın Halkalar
(2001) Gorentas, Necat
Bu çalışmada bazı küçük mertebeli gruplar için $M_A(G)$ yakın halkasının bir halka olup olmadığını belirleyip (A,$S_5$) regüler çifti için $M_A(S_5)$ in halka olmadığı gösterilmiştir.
Characterization of Central Units of Zan
(Korean Mathematical Soc, 2010) Bilgin, Tevfik; Gorentas, Necat; Kelebek, I. Gokhan
The structure of V(Z(ZA(n))) is known when n <= 6. If n = 5 or 6, then a complete set of generators of V(Z(ZA(n))) has been determined. In this study, it was shown that V(Z(ZA(n))) is trivial when n = 7, 8 or 9 and it is generated by a single unit u when n = 10 or 11. This unit u is characterized explicitly for n = 10 or 11 by using irreducible characters of A(n).
A Note on Characterization of Nu(Dn)
(Ieja-int Electronic Journal Algebra, 2008) Bilgin, Tevfik; Gorentas, Necat
In this paper construction of normalizer of D-n in V (ZD(n)) is reduced to construction of integral group ring of its cyclic subgroup. In a better expression, we have shown that N-u(D-n) = D-n x F, where F is a free abelian group with rank rho = 1/2 phi(n) - 1.
A Note on Simple Trinomial Units in U1(Zcp)
(Tubitak Scientific & Technological Research Council Turkey, 2020) Gorentas, Necat
In this paper, some new notions are defined about the unit group U-1(ZG) of a finite group G. Especially, notion of simple unit is defined by using the number of elements in its support and absolutely small coefficients of the unit. Units are classified as monomial, binomial, trinomial and k-nomial, level, unit with level l and simple unit. We have shown triviality of monomial units and nonexistence of binomial units in the unit group U-1(ZG) of an arbitrary finite group G. Some basic results and examples are posed about simple units and simple trinomial units in U-1(ZC(p)) of a cyclic group C-p, where p >= 5.
On the Average Degree of Characters with Odd or Even Degrees
(Elsevier, 2025) Aziziheris, Kamal; Gorentas, Necat; Sulaiman, Zinah Naser
Let acd(2 ' )(C) be the average degree of irreducible characters of C with odd degree. It has been proved that if acd(2 ')(C) < acd(2 ') (A(5)) = 3, then C is a solvable group. On the other hand, let acd(2)(C) be the average degree of linear characters and irreducible characters of C with even degree. It has been shown that if acd(2 ')(C) < acd(2 ')(A(5)) = 5/2, then C is a solvable group. In this paper, we improve these bounds and we show that if C is a finite group with acd(2 ') (C) < acd(2 ') (PSL(2, 7)) = 7/2, then either C is a solvable group or C has a chief factor isomorphic to A5. Also, we prove that if C is a finite group with acd(2)(C) < acd(2 ')(PSL(2, 8)) = 9/2, then either C is a solvable group or all minimal normal subgroups of C are abelian or isomorphic to A5. Clearly, these bounds are the best. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.