Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Michael Vaughan-Lee"'
Autor:
Michael Vaughan-Lee
Publikováno v:
International Journal of Group Theory, Vol 10, Iss 4, Pp 167-173 (2021)
There is a long-standing conjecture attributed to I. Schur that if $G$ is a finite group with Schur multiplier $M(G)$ then the exponent of $M(G)$ divides the exponent of $G$. In this note I give an example of a four generator group $G$ of order $5^{4
Externí odkaz:
https://doaj.org/article/b423ae482a764722b1c2c78b7607937b
Autor:
Michael Vaughan-Lee
Publikováno v:
International Journal of Group Theory, Vol 8, Iss 4, Pp 11-28 (2019)
Graham Higman published two important papers in 1960. In the first of these papers he proved that for any positive integer $n$ the number of groups of order $p^{n}$ is bounded by a polynomial in $p$, and he formulated his famo
Externí odkaz:
https://doaj.org/article/8462749c79144f90a28460037ac7d0f1
Autor:
Michael Vaughan-Lee
Publikováno v:
International Journal of Group Theory, Vol 4, Iss 4, Pp 25-42 (2015)
We prove that for p>7 there are p^4 +2p^3 +20p^2 +147p+(3p+29)gcd(p−1,3)+5gcd(p−1,4)+1246 groups of order p^8 with exponent p. If P is a group of order p^8 and exponent p, and if P has class c>1 then P is a
Externí odkaz:
https://doaj.org/article/b2e41997444e429f9523d403a5effdac
Autor:
Michael Vaughan-Lee
Publikováno v:
International Journal of Group Theory, Vol 2, Iss 3, Pp 49-61 (2013)
Graham Higman wrote two immensely important and in uential papers on enumerating p-groups in the late 1950s. The papers were entitled Enumerating p-groups I and II, and were published in the Proceedings of the London Mathematical Society in 1960. A c
Externí odkaz:
https://doaj.org/article/1fe0fc4745aa4944b8fc3f5dbf00d122
Autor:
Michael Vaughan-Lee
Publikováno v:
International Journal of Group Theory, Vol 1, Iss 4, Pp 65-79 (2012)
We investigate Graham Higman's paper Enumerating p-groups, II, in whichhe formulated his famous PORC conjecture. We look at the possibilities forturning his theory into a practical algorithm for computing the number of p-class two groups of order pn
Externí odkaz:
https://doaj.org/article/ab0babbdd28b47b79498c85983129751
Autor:
Seungjai Lee, Michael Vaughan-Lee
Publikováno v:
Experimental Mathematics. :1-7
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::43668ba6ab7d6236b4b68f228875ad52
https://doi.org/10.1080/10586458.2022.2062074
https://doi.org/10.1080/10586458.2022.2062074
Autor:
Bettina Eick, Michael Vaughan-Lee
Publikováno v:
Journal of Algebra. 545:198-212
Counting problems whose solution is PORC were introduced in a famous paper by Higman (1960). We consider two specific counting problems with PORC solutions: the number of isomorphism types of d-generator class-2 Lie algebras over F q (as a function i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e6a19f6b24ea009f71efd4bc68f2c61a
https://doi.org/10.1016/j.jalgebra.2019.02.034
https://doi.org/10.1016/j.jalgebra.2019.02.034
Autor:
Bettina Eick, Michael Vaughan-Lee
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783030521998
ICMS
ICMS
A symbolic Lie p-ring defines a family of Lie rings with \(p^n\) elements for infinitely many different primes p and a fixed positive integer n. Symbolic Lie p-rings are used to describe the classification of isomorphism types of nilpotent Lie rings
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f3d44608e67827bf0d2d71b4764edbfa
https://doi.org/10.1007/978-3-030-52200-1_13
https://doi.org/10.1007/978-3-030-52200-1_13
Autor:
Michael Vaughan-Lee
Publikováno v:
Journal of Algebra. 500:30-45
We investigate a family of 3-generator groups G ( p , x , y ) indexed by a prime p > 3 and integers x , y . The groups all have order p 7 and class 3. If x and y are coprime to p, then the order of the automorphism group of G ( p , x , y ) is one of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::88985bc5cff3a47b0793170a7d05cd71
https://doi.org/10.1016/j.jalgebra.2016.07.042
https://doi.org/10.1016/j.jalgebra.2016.07.042
Autor:
Michael Vaughan-Lee, George Havas
In 1957 D.R. Hughes published the following problem in group theory. Let G be a group and p a prime. Define Hp(G) to be the subgroup of G generated by all the elements of G which do not have order p. Is the following conjecture true: either Hp(G)=1,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::358fca12496c5b633dd931dee092e8f7
https://doi.org/10.1016/j.jalgebra.2009.04.011
https://doi.org/10.1016/j.jalgebra.2009.04.011