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Finite permutation groups and finite simple groups
 Bull. London Math. Soc
, 1981
"... In the past two decades, there have been farreaching developments in the problem of determining all finite nonabelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been ..."
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In the past two decades, there have been farreaching developments in the problem of determining all finite nonabelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of
The word problem for latticeordered groups
 Trans. Amer. Math. Soc
, 1983
"... To. W. W. Boone on the occasion of his 60 th birthday ..."
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To. W. W. Boone on the occasion of his 60 th birthday
A faithful representation of the singular braid monoid on three strands. in: Knots in Hellas ’98
 Delphi)), Ser. Knots Everything
, 1980
"... We show that a certain linear representation of the singular braid monoid SB3 is faithful. Furthermore we will give a second group theoretically motivated solution to the word problem in SB3. 1 ..."
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We show that a certain linear representation of the singular braid monoid SB3 is faithful. Furthermore we will give a second group theoretically motivated solution to the word problem in SB3. 1
W.Glass, Word problems, embeddings, and free products of rightordered groups with amalgamated subgroup
 Proc. London Math. Soc. 2009; doi: 10.1112/plms/pdp008
"... Dedicated to Graham Higman, in memoriam, with gratitude for his research. We use permutation groups to give necessary and sufficient conditions for the free product of right ordered groups with amalgamated subgroup to be right orderable. We obtain several consequences answering previously posed pr ..."
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Dedicated to Graham Higman, in memoriam, with gratitude for his research. We use permutation groups to give necessary and sufficient conditions for the free product of right ordered groups with amalgamated subgroup to be right orderable. We obtain several consequences answering previously posed problems and also prove the right orderable analogues of the Higman Embedding Theorem and the Boone–Higman Theorem. AMS Classification: 06F15, 20F60, 20B27, 20F10.
The word problem for the singular braid monoid
, 1999
"... We give a solution to the word problem for the singular braid monoid SBn. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically reprove a result of Fenn, Keyman and Rourke that the monoid emb ..."
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We give a solution to the word problem for the singular braid monoid SBn. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically reprove a result of Fenn, Keyman and Rourke that the monoid embeds into a group and we compute the cohomological dimension of this group. 1
EFFICIENT COMPUTATION IN GROUPS AND SIMPLICIAL COMPLEXES BY
"... Abstract. Using HNN extensions of the BooneBritton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time. Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators requi ..."
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Abstract. Using HNN extensions of the BooneBritton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time. Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators required to convert one word to another. The space bound is used to derive a PSPACEcomplete problem for a topological model of computation previously used to characterize NPcompleteness and REcompleteness. Introduction. The ability of mathematical systems to simulate computation has often been used to prove unsolvability results. The first, and most instructive, example was Post's simulation of Turing machines by finitely presented semigroups [10]. For each deterministic Turing machine M, Post constructs a semigroup T(M) on generators we shall call qa, sb, where a and A range over certain finite sets. An
GröbnerShirshov bases for some onerelator groups
, 2008
"... In this paper, we prove that twogenerator onerelator groups with depth less than or equal to 3 can be effectively embedded into a tower of HNNextensions in which each group has the effective standard normal form. We give an example to show how to deal with some general cases for onerelator group ..."
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In this paper, we prove that twogenerator onerelator groups with depth less than or equal to 3 can be effectively embedded into a tower of HNNextensions in which each group has the effective standard normal form. We give an example to show how to deal with some general cases for onerelator groups. By using the Magnus method and CompositionDiamond Lemma, we reprove the G. Higman, B. H. Neumann and H. Neumann’s embedding theorem.
Groups Geom. Dyn. 1 (2007), 1–20 Groups, Geometry, and Dynamics © European Mathematical Society
"... The isomorphism problem for residually torsionfree nilpotent groups ..."
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