Prime graphs of solvable groups

Ulvi , Muhammed İkbal
If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.


Ercan, Gülin; Ogut, Elif (2014-01-01)
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
Torsion Generators Of The Twist Subgroup
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01)
We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.
Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms
Ercan, Gülin; Khukhro, E. I. (2014-07-01)
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either |FH| is odd or |H| = 2). In the case where G is a finite p-group such that G = [G, F] it is proved that the rank of G is bounded ab...
Equivariant Picard groups of the moduli spaces of some finite Abelian covers of the Riemann sphere
Ozan, Yıldıray (2023-03-01)
In this note, following Kordek's work we will compute the equivariant Picard groups of the moduli spaces of Riemann surfaces with certain finite abelian symmetries.
Frobenius groups of automorphisms with almost fixed point free kernel
Ercan, Gülin (2019-03-01)
Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1.
Citation Formats
M. İ. Ulvi, “Prime graphs of solvable groups,” M.S. - Master of Science, Middle East Technical University, 2020.