Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element | Zendy

Patrick Kimani | Zendy; D. O. Adicka | Zendy

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Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element

Author(s) -

Patrick Kimani,

D. O. Adicka

Publication year - 2021

Publication title -

journal of advances in mathematics and computer science

Language(s) - English

Resource type - Journals

ISSN - 2456-9968

DOI - 10.9734/jamcs/2021/v36i730379

Subject(s) - centralizer and normalizer , coset , rank (graph theory) , action (physics) , mathematics , element (criminal law) , group (periodic table) , combinatorics , pure mathematics , discrete mathematics , algebra over a field , physics , quantum mechanics , political science , law

Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of centralizer of an elliptic element which is a non maximal subgroup . In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is q and the subdegrees are and .

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