Phases and conjugacy classes

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

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Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes

Advances in Mathematics ◽

10.1016/j.aim.2021.107688 ◽

2021 ◽

Vol 383 ◽

pp. 107688

Author(s):

Jeffrey Adams ◽

Xuhua He ◽

Sian Nie

Keyword(s):

Weyl Group ◽

Partial Orders ◽

Conjugacy Classes

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A classification of spherical conjugacy classes

Pacific Journal of Mathematics ◽

10.2140/pjm.2016.285.63 ◽

2016 ◽

Vol 285 (1) ◽

pp. 63-91

Author(s):

Mauro Costantini

Keyword(s):

Conjugacy Classes

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

Journal of Algebra and Its Applications ◽

10.1142/s0219498812501502 ◽

2012 ◽

Vol 12 (02) ◽

pp. 1250150 ◽

Cited By ~ 1

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.

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