Displaying similar documents to “A Non Solvable Operator Satisfying Condition ( ψ )

On computation of minimal free resolutions over solvable polynomial algebras

Huishi Li (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let A = K [ a 1 , ... , a n ] be a (noncommutative) solvable polynomial algebra over a field K in the sense of A. Kandri-Rody and V. Weispfenning [Non-commutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), 1–26]. This paper presents a comprehensive study on the computation of minimal free resolutions of modules over A in the following two cases: (1) A = p A p is an -graded algebra with the degree-0 homogeneous part A 0 = K ; (2) A is an -filtered algebra with the filtration { F p A } p determined by...

On solvability of finite groups with some s s -supplemented subgroups

Jiakuan Lu, Yanyan Qiu (2015)

Czechoslovak Mathematical Journal

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A subgroup H of a finite group G is said to be s s -supplemented in G if there exists a subgroup K of G such that G = H K and H K is s -permutable in K . In this paper, we first give an example to show that the conjecture in A. A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is s s -supplemented in G , and that G is solvable if and only if every Sylow subgroup of odd order of G is s s -supplemented in G . These results...

SCAP-subalgebras of Lie algebras

Sara Chehrazi, Ali Reza Salemkar (2016)

Czechoslovak Mathematical Journal

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A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP -subalgebra if there is a chief series 0 = L 0 L 1 ... L t = L of L such that for every i = 1 , 2 , ... , t , we have H + L i = H + L i - 1 or H L i = H L i - 1 . This is analogous to the concept of SCAP -subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP -subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.

On dicyclic groups as inner mapping groups of finite loops

Emma Leppälä, Markku Niemenmaa (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a finite group with a dicyclic subgroup H . We show that if there exist H -connected transversals in G , then G is a solvable group. We apply this result to loop theory and show that if the inner mapping group I ( Q ) of a finite loop Q is dicyclic, then Q is a solvable loop. We also discuss a more general solvability criterion in the case where I ( Q ) is a certain type of a direct product.

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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