Results 1  10
of
54,081
Solvable groups.
"... • Abelian groups are solvable. • N⊳Gwith N, G/N solvable ⇒ G solvable. (G solv ⇔∃N0 ⊳N1 ⊳ ···⊳Nk with Ni/Ni−1 abel) Rem. • Subgroups of solvable groups are solvable. • Quotients of solvable groups are solvable. • Semidirect products of solv grps are solv. • “Solvable grps have lots of normal subgrps ..."
Abstract
 Add to MetaCart
• Abelian groups are solvable. • N⊳Gwith N, G/N solvable ⇒ G solvable. (G solv ⇔∃N0 ⊳N1 ⊳ ···⊳Nk with Ni/Ni−1 abel) Rem. • Subgroups of solvable groups are solvable. • Quotients of solvable groups are solvable. • Semidirect products of solv grps are solv. • “Solvable grps have lots of normal
Quantum algorithms for solvable groups
 In Proceedings of the 33rd ACM Symposium on Theory of Computing
, 2001
"... ABSTRACT In this paper we give a polynomialtime quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group, r ..."
Abstract

Cited by 45 (1 self)
 Add to MetaCart
ABSTRACT In this paper we give a polynomialtime quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group
The entropy of solvable groups
, 2003
"... We prove that any finitely generated solvable group of zero entropy contains a nilpotent subgroup of finite index. In particular, any finitely generated solvable group of exponential growth is of uniformly exponential growth. ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We prove that any finitely generated solvable group of zero entropy contains a nilpotent subgroup of finite index. In particular, any finitely generated solvable group of exponential growth is of uniformly exponential growth.
NILPOTENT BLOCKS OF SOLVABLE GROUPS
"... Abstract. A well known result of Broue ́ and Puig gave necessary conditions for a block B of a finite group to be nilpotent. In this paper we have two goals. First, we explore potential sufficient conditions for blocks of solvable groups to be nilpotent. Secondly, we extend some known results about ..."
Abstract
 Add to MetaCart
Abstract. A well known result of Broue ́ and Puig gave necessary conditions for a block B of a finite group to be nilpotent. In this paper we have two goals. First, we explore potential sufficient conditions for blocks of solvable groups to be nilpotent. Secondly, we extend some known results
KTHEORY OF SOLVABLE GROUPS
, 2002
"... Abstract. We first prove that the Whitehead group of a torsionfree virtually solvable linear group vanishes. Next we make a reduction of the fibered isomorphism conjecture from virtually solvable groups to a class of virtually solvable Qlinear groups. Finally we prove an Ltheory analogue for elem ..."
Abstract
 Add to MetaCart
Abstract. We first prove that the Whitehead group of a torsionfree virtually solvable linear group vanishes. Next we make a reduction of the fibered isomorphism conjecture from virtually solvable groups to a class of virtually solvable Qlinear groups. Finally we prove an Ltheory analogue
Parallel Construction of Finite Solvable Groups
"... An algorithm for the construction of finite solvable groups of small order is given. A parallelized version under PVM is presented. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
An algorithm for the construction of finite solvable groups of small order is given. A parallelized version under PVM is presented.
ENDOTRIVIAL MODULES FOR pSOLVABLE GROUPS
"... Abstract. We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for psolvable groups, provided a conjecture can be proved about the case of pnilpotent groups. 1. ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Abstract. We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for psolvable groups, provided a conjecture can be proved about the case of pnilpotent groups. 1.
SOLVABLE GROUPS A NUMERICAL APPROACH
"... Abstract. We give all definitions related to solvable groups and show that any group of order up to 100 and not 60 is solvable. 1. ..."
Abstract
 Add to MetaCart
Abstract. We give all definitions related to solvable groups and show that any group of order up to 100 and not 60 is solvable. 1.
GEOMETRY AND DYNAMICS ON THE FREE SOLVABLE GROUPS
, 2000
"... In this paper we give a geometric realization of free solvable groups, and study its PoissonFurstenberg boundaries, we also discuss the construction of normal forms in the solvable groups. Free solvable groups were studied by algebraists in the 40s–50s in works by F.Hall, W.Magnus and others [9, 10 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In this paper we give a geometric realization of free solvable groups, and study its PoissonFurstenberg boundaries, we also discuss the construction of normal forms in the solvable groups. Free solvable groups were studied by algebraists in the 40s–50s in works by F.Hall, W.Magnus and others [9
on On Solvable Groups and Circulant Graphs
"... Let ϕ be Euler’s phi function. We prove that a vertextransitive graph Ɣ of order n, with gcd(n, ϕ(n)) = 1, is isomorphic to a circulant graph of order n if and only if Aut(Ɣ) contains a transitive solvable subgroup. As a corollary, we prove that every vertextransitive graph Ɣ of order n is isomor ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Let ϕ be Euler’s phi function. We prove that a vertextransitive graph Ɣ of order n, with gcd(n, ϕ(n)) = 1, is isomorphic to a circulant graph of order n if and only if Aut(Ɣ) contains a transitive solvable subgroup. As a corollary, we prove that every vertextransitive graph Ɣ of order n
Results 1  10
of
54,081