Classification of finite groups according to the number of conjugacy classes

1985 ◽  
Vol 51 (4) ◽  
pp. 305-338 ◽  
Author(s):  
Antonio Vera López ◽  
Juan Vera López
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes

Finite Groups with Some Subgroups of Given Order

2013 ◽  
Vol 20 (03) ◽  
pp. 457-462 ◽  
Author(s):  
Jiangtao Shi ◽  
Cui Zhang ◽  
Dengfeng Liang
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Solvable Groups ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Prime Power Order

Let [Formula: see text] be the class of groups of non-prime-power order or the class of groups of prime-power order. In this paper we give a complete classification of finite non-solvable groups with a quite small number of conjugacy classes of [Formula: see text]-subgroups or classes of [Formula: see text]-subgroups of the same order.

Classification of finite groups according to the number of conjugacy classes II

1986 ◽  
Vol 56 (2) ◽  
pp. 188-221 ◽  
Author(s):  
Antonio Vera López ◽  
Juan Vera López
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes

scholarly journals Elements of prime power order and their conjugacy classes in finite groups

2005 ◽  
Vol 78 (2) ◽  
pp. 291-295 ◽  
Author(s):  
László Héthelyi ◽  
Burkhard Külshammer
Keyword(s):  
Positive Integer ◽  
Finite Groups ◽  
Prime Power ◽  
Conjugacy Classes ◽  
Simple Groups ◽  
Prime Power Order ◽  
Finite Simple Groups

AbstractWe show that, for any positive integer k, there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes of elements of prime power order. This generalizes a result of E. Landau from 1903. The proof of our generalization makes use of the classification of finite simple groups.

scholarly journals A classification of spherical conjugacy classes

2016 ◽  
Vol 285 (1) ◽  
pp. 63-91
Author(s):  
Mauro Costantini
Keyword(s):  
Conjugacy Classes

A NOTE ON THE NUMBER OF ZEROS IN THE COLUMNS OF THE CHARACTER TABLE OF A GROUP

2012 ◽  
Vol 12 (02) ◽  
pp. 1250150 ◽  
Author(s):  
JINSHAN ZHANG ◽  
ZHENCAI SHEN ◽  
SHULIN WU
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Conjugacy Classes ◽  
Character Table ◽  
Number Of Zeros

The finite groups in which every irreducible character vanishes on at most three conjugacy classes were characterized [J. Group Theory13 (2010) 799–819]. Dually, we investigate the finite groups whose columns contain a small number of zeros in the character table.

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

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