scholarly journals GROUPS IN WHICH EVERY NON-CYCLIC SUBGROUP CONTAINS ITS CENTRALIZER

2014 ◽  
Vol 13 (05) ◽  
pp. 1350154 ◽  
Author(s):  
COSTANTINO DELIZIA ◽  
URBAN JEZERNIK ◽  
PRIMOŽ MORAVEC ◽  
CHIARA NICOTERA
Keyword(s):  
Cyclic Subgroup ◽  
Study Groups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Supersolvable Groups

We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also classify finite p-groups and finite simple groups with the above defined property.

scholarly journals A diameter bound for finite simple groups of large rank

2017 ◽  
Vol 95 (2) ◽  
pp. 455-474 ◽  
Author(s):  
Arindam Biswas ◽  
Yilong Yang
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Large Rank

scholarly journals New Beauville surfaces and finite simple groups

2013 ◽  
Vol 142 (3-4) ◽  
pp. 391-408 ◽  
Author(s):  
Shelly Garion ◽  
Matteo Penegini
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Beauville Surfaces

scholarly journals Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

2020 ◽  
Vol 23 (6) ◽  
pp. 999-1016
Author(s):  
Anatoly S. Kondrat’ev ◽  
Natalia V. Maslova ◽  
Danila O. Revin
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Exceptional Groups ◽  
Odd Index ◽  
Groups Of Lie Type

AbstractA subgroup H of a group G is said to be pronormal in G if H and {H^{g}} are conjugate in {\langle H,H^{g}\rangle} for every {g\in G}. In this paper, we determine the finite simple groups of type {E_{6}(q)} and {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

On Pronormal Subgroups in Finite Simple Groups

2018 ◽  
Vol 98 (2) ◽  
pp. 405-408 ◽  
Author(s):  
A. S. Kondrat’ev ◽  
N. V. Maslova ◽  
D. O. Revin
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups

scholarly journals Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

2001 ◽  
Vol 4 ◽  
pp. 135-169 ◽  
Author(s):  
Frank Lübeck
Keyword(s):  
Algebraic Groups ◽  
Small Degree ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Linear Algebraic Groups ◽  
Large Rank ◽  
Projective Representations ◽  
Computer Calculations ◽  
Simply Connected

AbstractThe author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l3, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

A new characterization of some finite simple groups

2015 ◽  
Vol 56 (1) ◽  
pp. 78-82 ◽  
Author(s):  
M. F. Ghasemabadi ◽  
A. Iranmanesh ◽  
F. Mavadatpour
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups
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