The Genus of a Group

White, Arthur T.

doi:10.1016/s0304-0208(01)80008-6

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 3 For Each Zero Of F (Z)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2005

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The genus of the finite group is the smallest genus of its Cayley graphs, that is, the smallest genus of all the closed orientable surfaces into which can be embedded the Cayley graph corresponding to some presentation for that group [3]. Maschke has classified the groups of genus 0 which are well known as the spherical space groups (see [16]). Viera Proulx has done the classification of all groups of genus 1 in [11].…”

Section: Theorem 3 For Each Zero Of F (Z)mentioning

confidence: 99%

Homomorphic images of △(2,3,11)

Mushtaq

Maqsood

2005

Discrete Mathematics

View full text Add to dashboard Cite

It is known that each conjugacy class of actions of P GL(2, Z) on F q ∪ {∞} can be represented by a coset diagram D( , q), where ∈ F q and q is a power of a prime p. In this paper, we are interested in parametrizing the conjugacy classes of actions of the infinite triangle group $(2, 3, 11) = x, y :depicting the conjugacy class of actions of $(2, 3, 11) on F q ∪{∞}. We have obtained conditions on and q which guarantee only those coset diagrams which depict homomorphic images of $(2, 3, 11) in P GL (2, q). We are interested in finding also when the coset diagrams for the actions of P GL(2, Z) on F q ∪ {∞} contain vertices on the vertical line of symmetry. It will enable us to show that for infinitely many values of q, the group P GL(2, q) has minimal genus, while also for infinitely many q, the group P SL(2, q) is an H * -group.

show abstract

Section: Theorem 3 For Each Zero Of F (Z)mentioning

confidence: 99%