FREE SEMIGROUP IN THE GROUP OF AUTOMORPHISMS OF THE FREE BURNSIDE GROUP

2005 ◽  
Vol 33 (2) ◽  
pp. 539-547 ◽  
Author(s):  
E.A. Cherepanov
Keyword(s):  
Free Semigroup ◽  
Group Of Automorphisms ◽  
Free Burnside Group

scholarly journals THE GROUPS OF AUTOMORPHISMS ARE COMPLETE FOR FREE BURNSIDE GROUPS OF ODD EXPONENTS n ≥ 1003

2013 ◽  
Vol 23 (06) ◽  
pp. 1485-1496 ◽  
Author(s):  
V. S. ATABEKYAN
Keyword(s):  
Normal Subgroup ◽  
Free Groups ◽  
Group Of Automorphisms ◽  
Burnside Groups ◽  
Free Burnside Group ◽  
Trivial Center ◽  
Groups Of Automorphisms ◽  
Group B ◽  
Inner Automorphisms ◽  
Automorphism Tower

It is proved that the group of automorphisms Aut (B(m, n)) of the free Burnside group B(m, n) is complete for every odd exponent n ≥ 1003 and for any m > 1, that is, it has a trivial center and any automorphism of Aut (B(m, n)) is inner. Thus, the automorphism tower problem for groups B(m, n) is solved and it is showed that it is as short as the automorphism tower of the absolutely free groups. Moreover, the group of all inner automorphisms Inn (B(m, n)) is the unique normal subgroup in Aut (B(m, n)) among all its subgroups, which are isomorphic to free Burnside group B(s, n) of some rank s.

scholarly journals Operator Algebras with Unique Preduals

2011 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Alex Wright
Keyword(s):  
Banach Space ◽  
Operator Algebra ◽  
Free Semigroup ◽  
Operator Algebras ◽  
Compact Operators ◽  
Semigroup Algebra ◽  
Dense Subalgebra

AbstractWe show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

THE WORD PROBLEM FOR THE RELATIVELY FREE SEMIGROUP SATISFYING Tm=Tm+n WITH m≥3

1993 ◽  
Vol 03 (03) ◽  
pp. 335-347 ◽  
Author(s):  
V.S. GUBA
Keyword(s):  
Word Problem ◽  
Free Semigroup

Let m≥3, n≥1. In this article we show that the word problem for the relatively free Burnside semigroup satisfying Tm=Tm+n, is decidable.

scholarly journals Elements of finite order in Stone-Čech compactifications

1993 ◽  
Vol 36 (1) ◽  
pp. 49-54 ◽  
Author(s):  
John Baker ◽  
Neil Hindman ◽  
John Pym
Keyword(s):  
Compact Group ◽  
Finite Order ◽  
Free Semigroup ◽  
Continuous Homomorphism ◽  
Discrete Topology ◽  
Natural Extensions ◽  
Finite Sums

Let S be a free semigroup (on any set of generators). When S is given the discrete topology, its Stone-Čech compactification has a natural semigroup structure. We give two results about elements p of finite order in βS. The first is that any continuous homomorphism of βS into any compact group must send p to the identity. The second shows that natural extensions, to elements of finite order, of relationships between idempotents and sequences with distinct finite sums, do not hold.

scholarly journals Constructions for arc-transitive digraphs

1995 ◽  
Vol 59 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Marston Conder ◽  
Peter Lorimer ◽  
Cheryl Praeger
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Finite Groups ◽  
Transitive Permutation Group ◽  
Group Of Automorphisms ◽  
Representations Of Finite Groups ◽  
Regular Digraph

AbstractA number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.

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