The Groups and Nilpotent Lie Rings of Order p8 with Maximal Class

被引：0

作者：

Lee, Seungjai ^{[1
]}

Vaughan-Lee, Michael ^{[2
]}

机构：

[1] Seoul Natl Univ, Res Inst Basic Sci, Seoul 08826, South Korea

[2] Univ Oxford, Christ Church, Oxford, England

来源：

EXPERIMENTAL MATHEMATICS | 2022年

基金：

新加坡国家研究基金会;

关键词：

p-group; maximal class; Lie p-ring; Higman's PORC conjecture;

D O I：

10.1080/10586458.2022.2062074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify and count the nilpotent Lie rings of order p(8) with maximal class for p >= 5. This also provides a classification of the groups of order p(8) with maximal class for p >= 11 via the Lazard correspondence. We also record the number of nilpotent Lie rings/groups of order p(n) with maximal class for n <= 7 from currently known data and discuss its asymptotic behavior as n grows and its potential connection to Higman's PORC conjecture.

引用

页码：247 / 253

页数：7

共 12 条

[1] Bagnera G, 1898, ANN MAT PUR APPL, V3, P137, DOI [10.1007/BF02419191, DOI 10.1007/BF02419191]
[2] A millennium project: Constructing small groups
Besche, HU
Eick, B
O'Brien, EA
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2002, 12 (05) : 623 - 644
[3] The Magma algebra system .1. The user language
Bosma, W
Cannon, J
Playoust, C
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
[4] Cicalo S., 2019, LIERING COMPUTING FI
[5] Eick B, 2018, LIEPRING DATABASE AL
[6] Higman's PORC conjecture for a family of groups
Evseev, Anton
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2008, 40 : 415 - 431
[7] Higman G., 1960, Proc. London Math. Soc., V10, P566, DOI 10.1112/plms/s3-10.1. 566
[8] Groups and nilpotent Lie rings whose order is the sixth power of a prime
Newman, MF
O'Brien, EA
Vaughan-Lee, MR
[J]. JOURNAL OF ALGEBRA, 2004, 278 (01) : 383 - 401
[9] The groups with order p7 for odd prime p
O'Brien, EA
Vaughan-Lee, MR
[J]. JOURNAL OF ALGEBRA, 2005, 292 (01) : 243 - 258
[10] THE P-GROUP GENERATION ALGORITHM
OBRIEN, EA
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1990, 9 (5-6) : 677 - 698

← 1 2 →