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A note on growth sequences of finite simple groups

Ahmad Erfanian, James Wiegold
1995 Bulletin of the Australian Mathematical Society  
However, the lemma is sufficient to enable us to estabish our final result. D THEOREM 5 . Let {A a }a€J be an infinite set of finite non-abelian simple groups of spread one.  ...  Wiegold [2] Clearly, ca(H) is sometimes zero, but we believe it to be non-zero for every nontrivial subgroup of a finite simple group A. (Equivalently, A has spread one in the parlance of [1] .)  ... 
doi:10.1017/s0004972700014337 fatcat:ah4xulu6ybeixd2uzzjqm4dcna

Page 5866 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
Determine the exact spread for all finite simple groups. (4) For a finite simple group G, the probability P(G) that two (or three) randomly chosen elements generates the whole group G tends to 1 as the  ...  The au- thor mentions many applications of the classification of finite simple groups.  ... 

The exact spread of M12 is 9 [article]

Ben Fairbairn
2010 arXiv   pre-print
The precise value of the exact spread of a simple group is known in very few cases.  ...  The group G has exact spread r if it has spread r but not r + 1. The case where G is a finite simple group is particularly interesting since it is known that in this case the spread is at least 2.  ...  Even so, the precise value of the exact spread of most finite simple groups remains open.  ... 
arXiv:0909.2174v2 fatcat:sugm2nbo3nfptpkqfz23ytozh4

Page 4481 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
; Los Angeles, CA); Shalev, Aner (IL-HEBR-IM; Jerusalem) On the spread of finite simple groups.  ...  In the present paper the authors obtain upper and lower bounds for the spread of some finite simple groups such as the alternating and the orthogonal groups in odd dimension.  ... 

Page 6366 of Mathematical Reviews Vol. , Issue 87k [page]

1987 Mathematical Reviews  
The author calls two packings “2-orthogonal” if any spread of one intersects any spread of the other in at most two lines. The main result of the paper is to construct q — 2 mutually  ...  “We give some limitations on the possible actions a simple group can have on a finite translation plane, similar to those given by G. Mason [ibid., 333-346; MR 84j:20042] and D. A. Foulser et al.  ... 

Simple groups, generation and probabilistic methods [article]

Timothy C. Burness
2017 arXiv   pre-print
In this survey article we discuss some of the extraordinary generation properties of simple groups, focussing on topics such as random generation, (a,b)-generation and spread, as well as highlighting the  ...  It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years.  ...  In particular, the spread of a finite simple group can be arbitrarily large. They also observe that the spread of odd degree alternating groups is radically different.  ... 
arXiv:1710.10434v1 fatcat:l7knkpjf3ved3okyow5hjxp7mm

On the structure of ℵ0-categorical groups

A.B Apps
1983 Journal of Algebra  
Thus any &categorical group has finite conjugate spread. We note that the property of having finite conjugate spread is inherited by quotient groups.  ...  The result follows. 1 In essence, these corollaries show that, in the class of groups with finite conjugate spread, extensions of a Boolean power of a finite simple nonabelian group by some other locally  ... 
doi:10.1016/0021-8693(83)90192-8 fatcat:zgtywcf4bjcerejminpq3secz4

On the Exact Spread of Sporadic Simple Groups

John Bradley, Jamshid Moori
2007 Communications in Algebra  
., 2-Generations of the sporadic simple groups, Ph.D thesis, University of Natal, 1996. [3] Ganief, M.S., Moori, J., On the spread of the sporadic simple groups, Communications in Algebra 29 (2001), 3239  ...  The present paper deals with the search for reasonable upper bounds for the exact spread of the sporadic simple groups. [ 1 ] 1 Brenner, J.L., Wiegold, J., Two-generator groups, I. Michigan Math.  ... 
doi:10.1080/00927870701327765 fatcat:wmko7hk5tfdmrayliy2naqpgcy

The exact spread of M23 is 8064 [article]

Ben Fairbairn
2010 arXiv   pre-print
,x8064 is a set of distinct non-trivial elements of the sporadic simple Mathieu group M23 then there exists an element y such that y,x_i generates the whole group for every 0<i<8065 and that no larger  ...  set of distinct elements of M23 has this property.  ...  The precise value of the exact spread of a finite simple group is known in very few cases. Here we prove the following.  ... 
arXiv:1008.1503v1 fatcat:yili5v66izaddl6fag3p62rmcm

Page 2580 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Also, strong results are available using the classification of finite simple groups [F. Buekenhout and H. J. Van Maldeghem, Geom.  ...  It remains an open question as to whether or not all finite generalized quadrangles all points of which are elation points can be classified without the classification of the finite simple groups.  ... 

Page 7249 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
It seems to be a very difficult problem to achieve this without the classi- fication of finite simple groups.  ...  Salzmann on the occasion of his 70th birthday. Geom. Dedicata 83 (2000), no. 1-3, 207-210. Using the classification of finite simple groups, F. Buekenhout and H. J. Van Maldeghem [Geom.  ... 

Page 3357 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
ISBN 3-11-013783-6 The book deals with certain “concrete” aspects of the represen- tation theory of finite (almost) simple groups, namely with the realization of certain classes of these groups as automorphism  ...  automorphism group transitive on the nonzero vectors in Fo" : The known classification of such spreads (these are unique except for p” = 27) then gives the desired result.  ... 

Page 1159 of Mathematical Reviews Vol. 51, Issue 4 [page]

1976 Mathematical Reviews  
Z. 83 (1964), 72-84, Theorem 1; MR 28 #3088] on the existence of normal complements of sections of finite groups.  ...  The result is a step towards a classifi- cation of simple groups with a maximal intersection of Sylow 2- subgroups being of 2-rank one. J. L. Alperin (Chicago, Ill.)  ... 

Simple collineation groups with perspectivities of finite translation planes

Chat Yin Ho
2004 Journal of Algebra  
We also thank the referee for his insightful suggestions.  ...  Some words on the notations. From now on, in this paper planes and groups will have finite cardinalities. A member of a spread is called a fiber.  ...  From now on we use the term a simple group to mean a nonabelian simple group.  ... 
doi:10.1016/j.jalgebra.2004.01.013 fatcat:bwwsszhgend4bo7kz6xk7cbqyq

Page 6453 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
of all finite simple groups.  ...  Evgenii P- Vdovin (1-PADV-PM,; Padua) 2002i:20025 20D08 20P05 Ganief, Shahiem (SA-WCAP; Bellville) ; Moori, Jamshid (SA-NTL2; Pietermaritzburg) On the spread of the sporadic simple groups.  ... 
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