scholarly journals Fixed point ratios in actions of finite classical groups, I

2007 ◽  
Vol 309 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Timothy C. Burness
Keyword(s):  
Fixed Point ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals Generation of finite classical groups by pairs of elements with large fixed point spaces

2015 ◽  
Vol 421 ◽  
pp. 56-101 ◽  
Author(s):  
Cheryl E. Praeger ◽  
Ákos Seress ◽  
Şükrü Yalçınkaya
Keyword(s):  
Fixed Point ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals Elements in finite classical groups whose powers have large 1-Eigenspaces

2014 ◽  
Vol Vol. 16 no. 1 ◽  
Author(s):  
Alice Niemeyer ◽  
Cheryl Praeger
Keyword(s):  
Fixed Point ◽  
60Th Birthday ◽  
Classical Groups ◽  
Special Issue ◽  
Arbitrary Characteristic ◽  
Recognition Algorithms ◽  
Finite Classical Groups ◽  
International Audience

Special issue in honor of Laci Babai's 60th birthday International audience We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point subspace and acts irreducibly on a complement of it. The estimates are used in complexity analyses of new recognition algorithms for finite classical groups in arbitrary characteristic.

scholarly journals Power series coefficients for probabilities in finite classical groups

2006 ◽  
Vol 305 (2) ◽  
pp. 1212-1237
Author(s):  
John R. Britnell ◽  
Jason Fulman
Keyword(s):  
Power Series ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals The sylow 2-subgroups of the finite classical groups

1964 ◽  
Vol 1 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Roger Carter ◽  
Paul Fong
Keyword(s):  
Classical Groups ◽  
Finite Classical Groups

RANDOM (r, s)-GENERATION OF FINITE CLASSICAL GROUPS

2002 ◽  
Vol 34 (2) ◽  
pp. 185-188 ◽  
Author(s):  
MARTIN W. LIEBECK ◽  
ANER SHALEV
Keyword(s):  
Classical Groups ◽  
Large Rank ◽  
Finite Classical Groups

A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| → ∞.

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