Browsing by Author "Bilgin, Tevfik"

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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 Characterization of the Unit Group in Z[T X C2]
(Korean Mathematical Soc, 2016) Bilgin, Tevfik; Kusmus, Omer; Low, Richard M.
Describing the group of units U(ZG) of the integral group ring SG, for a finite group G, is a classical and open problem. In this note, we show that U-1(Z[T x C-2]) similar or equal to [F-97 x F-5] x [T x C-2], where T = < a, b : a(6) = 1, a(3) = b(2), ba = a(5)b > and F-97, F-97 are free groups of ranks 97 and 5, respectively.
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.