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THE SUBGROUP ALGORITHM FOR GENERATING UNIFORM RANDOM VARIABLES
Subgroup algorithm to generate unified random variable
2015/7/14
THE SUBGROUP ALGORITHM FOR GENERATING UNIFORM RANDOM VARIABLES.
Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
Cayley graph hamiltonian cycle commutator subgroup
2012/5/9
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
Upgrading Subgroup Triple Product Property Triples
Subgroup Triple Product Property Triples Group Theory
2011/9/23
Abstract: In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as...
A note on the Triple Product Property subgroup capacity of finite groups
Triple Product Property finite groups Group Theory
2011/9/23
Abstract: In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the ...
A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting
Polynomial recurrences symbolic summation subgroup numbers free subgroup numbers Catalan numbers
2011/9/1
Abstract: We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-C...
We give a list of finite groups containing all finite groups G such that the group of units ZG∗ of the integral group ring ZG is subgroup separable. There are only two types of these groups G fo...
On subgroup conjugacy separability in the class of virtually free groups
subgroup conjugacy separability class of virtually free groups
2011/2/25
A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that t...
On the $p$-adic closure of a subgroup of rational points on an Abelian variety
$p$-adic closure subgroup of rational points Abelian variety
2011/2/24
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
Centralizer of the elementary subgroup of an isotropic reductive group
Centralizer of the elementary subgroup isotropic reductive group
2011/1/17
Let R be a commutative ring with 1, and let G be an isotropic reductive algebraic group over R. In [5] Victor Petrov and the second author introduced a notion of an elementary subgroup E(R) of the gro...
The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n)
partial bases for F_n finite generation Torelli subgroup of Aut(F_n)
2011/1/19
We study the complex of partial bases of a free group, which is an analogue for Aut(Fn)
of the curve complex for the mapping class group. We prove that it is connected and simply
connected, and we a...
A new subgroup lattice characterization of finite solvable groups
subgroup lattice characterization solvable groups
2010/11/18
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maxi...
Subgroup S-commutativity degree of finite groups
Subgroup commutativity degree subgroup S–commutativity degree Sylow subgroups
2010/12/3
In a recent contribution, Tˇarnˇauceanu has introduced the subgroup commutativity degree of a finite group,adapting to the context of the lattice theory some ideas and some techniques, which were know...
Subgroup Distortion in Wreath Products of Cyclic Groups
Subgroup Distortion Wreath Products of Cyclic Groups
2010/12/10
We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function bound...
The structure of infinite 2-groups with a unique 2-element subgroup
infinite 2-groups unique 2-element subgroup
2010/11/26
We prove that each infinite 2-group G with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group C21 or to the infinite group of generalized quaternions Q21. The
latter group is...
Quotients by actions of the derived group of a maximal unipotent subgroup
Quotients derived group of a maximal unipotent subgroup
2010/12/9
The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple
algebraic group with Lie algebra g. Fix a maximal unipotent subgroup U ⊂ G and a maximal torus T of ...