Computation in nilpotent groups (application)

Bayes, Adam; Kautský, Jaroslav; Wamsley, J. W.

doi:10.1007/bfb0065161

Cited by 14 publications

(11 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then in [2], Bachmuth and Mochizuki constructed an example of a 3-Engel group of exponent 5 that is not soluble. By looking at a power commutator presentation of the free 3-generator group of exponent 4 [3], one sees that every group of exponent 4 is central by 4-Engel. As groups of exponent 4 need not be soluble [18], the same is true for 4-Engel groups of exponent 4.…”

Section: Theorem W Every Residually Finite N-engel Group Is Locally mentioning

confidence: 99%

“…As B(∞, 4) is not (2, 4) nilpotent this is not immediately clear. However, one can see from a power commutator presentation of the free 3-generator group of exponent 4 that B(∞, 4)/Z(B(∞, 4)) is (2, 4) nilpotent [3]. So 3d − 3 is also the best upper bound when d = 2.…”

Section: Proposition 22 There Exists a Positive Integer S = S(n) Sumentioning

confidence: 99%

“…We know that the normal closure of the third power of any element is abelian of exponent 3. Let g, a 1 , a 2 , a 3 In other words H is the verbal subgroup generated by the word (x…”

mentioning

confidence: 99%

See 2 more Smart Citations

On locally finite 𝑝-groups satisfying an Engel condition

Abdollahi

Traustason²

2002

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. For a given positive integer n and a given prime number p, let r = r(n, p) be the integer satisfying p r−1 < n ≤ p r . We show that every locally finite p-group, satisfying the n-Engel identity, is (nilpotent of n-bounded class)-by-(finite exponent) where the best upper bound for the exponent is either p r or p r−1 if p is odd. When p = 2 the best upper bound is p r−1 , p r or p r+1 . In the second part of the paper we focus our attention on 4-Engel groups. With the aid of the results of the first part we show that every 4-Engel 3-group is soluble and the derived length is bounded by some constant.

show abstract

Section: Theorem W Every Residually Finite N-engel Group Is Locally mentioning

confidence: 99%

Section: Proposition 22 There Exists a Positive Integer S = S(n) Sumentioning

confidence: 99%

See 1 more Smart Citation

On locally finite 𝑝-groups satisfying an Engel condition

Abdollahi

Traustason²

2002

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Effective algorithms for determining p-quotients were originated by the work of Macdonald (1973Macdonald ( , 1974. His techniques were later extended by Wamsley (1974), Bayes et al (1974), Newman (1976) and Havas and Newman (1980). Nickel (1994) developed and implemented an algorithm to compute the nilpotent quotients for finitely presented groups.…”

Section: Definition 13 Given a Finite Presentation Of A Group G A mentioning

confidence: 99%

A Polycyclic Quotient Algorithm

1998

Journal of Symbolic Computation

View full text Add to dashboard Cite

“…Recently Bayes, Kau+sky and Wamsley [3] have determined that the order of B(k, 3) is 2 6 9 and that the group has class 7 by computing a consistent commutator power presentation for that group. Work is currently in progress on computing a consistent commutator power presentation for B(U, U) (Alford,Havas and Newman [2]).…”

mentioning

confidence: 99%