Solvable groups with isomorphic group algebras
نویسندگان
چکیده
منابع مشابه
Non-isomorphic C∗-algebras with Isomorphic Unitary Groups
Dye, [Ann. of Math. (2) 61 (1955), 73–89] proved that the discrete unitary group in a factor determines the algebraic type of the factor. Afterwards, for a large class of simple unital C∗-algebras, Al-Rawashdeh, Booth and Giordano [J. Funct. Anal. 262 (2012), 4711–4730] proved that the algebras are ∗-isomorphic if and only if their unitary groups are isomorphic as abstract groups. In this paper...
متن کاملGroup Rings with Solvable «-engel Unit Groups'
Let KG be the group ring of a group G over a field of characteristic p > 0, p ^ 2, 3. Suppose G contains no element of order p (if p > 0). Group algebras KG with unit group U(KG) solvable and n-Engel are characterized. Let ATG be the group ring of a group G over a field K of characteristic p > 0 and let U(KG) denote its group of units. Several authors including Bateman [1], Bateman and Coleman ...
متن کاملClassification of solvable groups with a given property
In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.
متن کاملSolvable Lie algebras with $N(R_n,m,r)$ nilradical
In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.
متن کاملA Note on Isomorphic Commutative Group Algebras over Certain Rings
Suppose G is an abelian group and R is a commutative ring with 1 of char(R) = 0. It is proved that if G is R-favorable torsion and RH and RG are R-isomorphic group algebras for some group H , then H is Rfavorable torsion abelian if and only if either inv(R) = ∅ or inv(R) = ∅ and R is an ND-ring. This strengthens results due to W. Ullery (Comm. Algebra, 1986), (Rocky Mtn. J. Math., 1992) and (Co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1966
ISSN: 0025-5645
DOI: 10.2969/jmsj/01840394