ABSTRACT
The action of Projective Special Linear group PSL(2; q) on the cosets of
its subgroups is studied. Primitive permutation representations of PSL(2; q)
have been previously studied by Tchuda (1986), Bon and Cohen (1989) and
Kamuti (1992). In particular, the permutation representations on the cosets
of Cq1
k
; Cq+1
k
; Pq; A4 and D2(q1)
k
are studied. In the case where it was
previously done, we employ a dierent method or otherwise quote the results
for completeness purpose. Thus, this thesis deals with determination of disjoint
cycle structures, cycle indices, ranks and subdegrees when PSL(2; q) acts on the
cosets of its ve subgroups mentioned above. Cycle indices are obtained using
a method coined by Kamuti (1992), while ranks and subdegrees are determined
using two methods, either algebraic arguments, use of table of marks, a method
proposed by Ivanov et al. (1983) or both. Subdegrees of PSL(2; q) acting on
the cosets of its cyclic subgroup Cq1
k
are shown to be 1(2); (q 1)(q+2) when
q is even and 1(2); ( q1
2 )(2q+4) when q is odd using reduced pair group action.
In this representation, the number of self-paired suborbits is determined to be
q + 2 when p = 2, q + 3 when q 1 (mod 4) and q + 1 when q 1 (mod 4).
The suborbit (1;1) is shown to be paired with (0;1). A method for the
construction of suborbital graphs corresponding to the action PSL(2; q) on the
cosets of Cq1 is given. The constructed suborbital graphs that are directed are shown to be of girth three.
Bunyasi, M (2021). Cycle Indices, Subdegrees And Suborbital Graphs Of Psl(2,Q) Acting On The Cosets Of Some Of Its Subgroups. Afribary. Retrieved from https://tracking.afribary.com/works/cycle-indices-subdegrees-and-suborbital-graphs-of-psl-2-q-acting-on-the-cosets-of-some-of-its-subgroups
Bunyasi, Magero "Cycle Indices, Subdegrees And Suborbital Graphs Of Psl(2,Q) Acting On The Cosets Of Some Of Its Subgroups" Afribary. Afribary, 27 May. 2021, https://tracking.afribary.com/works/cycle-indices-subdegrees-and-suborbital-graphs-of-psl-2-q-acting-on-the-cosets-of-some-of-its-subgroups. Accessed 24 Nov. 2024.
Bunyasi, Magero . "Cycle Indices, Subdegrees And Suborbital Graphs Of Psl(2,Q) Acting On The Cosets Of Some Of Its Subgroups". Afribary, Afribary, 27 May. 2021. Web. 24 Nov. 2024. < https://tracking.afribary.com/works/cycle-indices-subdegrees-and-suborbital-graphs-of-psl-2-q-acting-on-the-cosets-of-some-of-its-subgroups >.
Bunyasi, Magero . "Cycle Indices, Subdegrees And Suborbital Graphs Of Psl(2,Q) Acting On The Cosets Of Some Of Its Subgroups" Afribary (2021). Accessed November 24, 2024. https://tracking.afribary.com/works/cycle-indices-subdegrees-and-suborbital-graphs-of-psl-2-q-acting-on-the-cosets-of-some-of-its-subgroups