(3, 𝑞, 𝑟)-generations of Fischer's sporadic group Fi′24
Author:
Ali Faryad1, Ibrahim Mohammed Ali Faya2, Woldar Andrew3
Affiliation:
1. Department of Mathematics and Statistics , College of Science , Al Imam Mohammad Ibn Saud Islamic University (IMSIU) , P.O. Box 90950 , Riyadh 11623 , Saudi Arabia 2. Department of Mathematics , Najran University , Najran , Saudi Arabia 3. Department of Mathematics and Statistics , Villanova University , Villanova , PA 19085 , USA
Abstract
Abstract
A group G is said to be
(
l
,
m
,
n
)
{(l,m,n)}
-generated if it can be generated by two suitable elements x and y such that
o
(
x
)
=
l
{o(x)=l}
,
o
(
y
)
=
m
{o(y)=m}
and
o
(
x
y
)
=
n
{o(xy)=n}
.
In [J. Moori,
(
p
,
q
,
r
)
{(p,q,r)}
-generations for the Janko groups
J
1
{J_{1}}
and
J
2
{J_{2}}
,
Nova J. Algebra Geom. 2 1993, 3, 277–285],
J. Moori posed the problem of finding all triples of distinct primes
(
p
,
q
,
r
)
{(p,q,r)}
for which a finite non-abelian simple group is
(
p
,
q
,
r
)
{(p,q,r)}
-generated.
In the present article, we partially answer this question for Fischer’s largest sporadic simple group
Fi
24
′
{\mathrm{Fi}_{24}^{\prime}}
by determining all
(
3
,
q
,
r
)
{(3,q,r)}
-generations, where q and r are prime divisors of
|
Fi
24
′
|
{\lvert\mathrm{Fi}_{24}^{\prime}\rvert}
with
3
<
q
<
r
{3<q<r}
.
Funder
King Abdulaziz City for Science and Technology
Publisher
Walter de Gruyter GmbH
Subject
Algebra and Number Theory
Reference31 articles.
1. F. Ali,
On the ranks of O’N and Ly,
Discrete Appl. Math. 155 (2007), no. 3, 394–399. 2. F. Ali,
On the ranks of Fi22{\mathrm{Fi}_{22}},
Quaest. Math. 37 (2014), no. 4, 591–600. 3. F. Ali and M. Al-Kadhi,
Generating pairs for the Fischer group Fi23{\mathrm{Fi}_{23}},
submitted. 4. F. Ali, M. Al-Kadhi, A. Aljouiee and M. Ibrahim,
2-generations of finite simple groups in GAP,
2016 International Conference on Computational Science and Computational Intelligence (CSCI),
IEEE Press, Piscataway (2016), 1339–1344. 5. F. Ali, M. Ibrahim and A. Woldar,
On (2,3){(2,3)}-generation of Fischer’s largest sporadic simple group Fi24′{\mathrm{Fi}_{24}^{\prime}},
submitted.
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1. ON THE RANKS OF FISCHER GROUP Fi23;JP Journal of Algebra, Number Theory and Applications;2019-05-20
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