Groups and nilpotent Lie rings whose order is the sixth power of a prime

M. F. Newman; E. A. O'Brien; Michael R. Vaughan-Lee

doi:10.1016/j.jalgebra.2003.11.012

Groups and nilpotent Lie rings whose order is the sixth power of a prime

M. F. Newman^*, E. A. O'Brien, Michael R. Vaughan-Lee

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

Abstract

We prove that there are 3p²+39p+344+24gcd(p-1,3)+11gcd (p-1,4)+2gcd(p-1,5) isomorphism types of groups and nilpotent Lie rings with order p⁶ for every prime p≥5. We establish the result, and power-commutator presentations for the groups, in various ways. The most novel method constructs product presentations for nilpotent Lie rings with order p⁶ and then uses the Baker-Campbell-Hausdorff formula to construct power-commutator presentations for the corresponding groups. Public access to the group presentations is provided via a database distributed with computer algebra systems.

Original language	English
Pages (from-to)	383-401
Number of pages	19
Journal	Journal of Algebra
Volume	278
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2003.11.012
Publication status	Published - 1 Aug 2004

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10.1016/j.jalgebra.2003.11.012

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abstract = "We prove that there are 3p2+39p+344+24gcd(p-1,3)+11gcd (p-1,4)+2gcd(p-1,5) isomorphism types of groups and nilpotent Lie rings with order p6 for every prime p≥5. We establish the result, and power-commutator presentations for the groups, in various ways. The most novel method constructs product presentations for nilpotent Lie rings with order p6 and then uses the Baker-Campbell-Hausdorff formula to construct power-commutator presentations for the corresponding groups. Public access to the group presentations is provided via a database distributed with computer algebra systems.",

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AU - Newman, M. F.

AU - O'Brien, E. A.

AU - Vaughan-Lee, Michael R.

PY - 2004/8/1

Y1 - 2004/8/1

N2 - We prove that there are 3p2+39p+344+24gcd(p-1,3)+11gcd (p-1,4)+2gcd(p-1,5) isomorphism types of groups and nilpotent Lie rings with order p6 for every prime p≥5. We establish the result, and power-commutator presentations for the groups, in various ways. The most novel method constructs product presentations for nilpotent Lie rings with order p6 and then uses the Baker-Campbell-Hausdorff formula to construct power-commutator presentations for the corresponding groups. Public access to the group presentations is provided via a database distributed with computer algebra systems.

AB - We prove that there are 3p2+39p+344+24gcd(p-1,3)+11gcd (p-1,4)+2gcd(p-1,5) isomorphism types of groups and nilpotent Lie rings with order p6 for every prime p≥5. We establish the result, and power-commutator presentations for the groups, in various ways. The most novel method constructs product presentations for nilpotent Lie rings with order p6 and then uses the Baker-Campbell-Hausdorff formula to construct power-commutator presentations for the corresponding groups. Public access to the group presentations is provided via a database distributed with computer algebra systems.

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VL - 278

SP - 383

EP - 401

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Groups and nilpotent Lie rings whose order is the sixth power of a prime

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