On (t + ...)-transitive Permutation Groups.
John P.J. McDermott (1976)
Mathematische Zeitschrift
Steve Ligh (1972)
Monatshefte für Mathematik
K. Corrádi, S. Szabó (1990)
Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry
Hashemi, M. (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
Alireza Khalili Asboei, Seyed Sadegh Salehi Amiri (2022)
Czechoslovak Mathematical Journal
We prove that if the average number of Sylow subgroups of a finite group is less than and not equal to , then is solvable or . In particular, if the average number of Sylow subgroups of a finite group is , then , where is the largest normal solvable subgroup of . This generalizes an earlier result by Moretó et al.
Joseph A. Gallian (1972)
Mathematische Zeitschrift
Kuznetsov, A.A., Filippov, K.A. (2010)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
Thomas Diethelm (1983)
Commentarii mathematici Helvetici
Doostie, H., Campbell, P.P. (2006)
International Journal of Mathematics and Mathematical Sciences
Azam Babai, Behrooz Khosravi (2012)
Czechoslovak Mathematical Journal
Let be a finite group. The prime graph of is a graph whose vertex set is the set of prime divisors of and two distinct primes and are joined by an edge, whenever contains an element of order . The prime graph of is denoted by . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if is a finite group such that , where , then has a unique nonabelian composition factor isomorphic to or .
Herbert Dietzsch (1971)
Rendiconti del Seminario Matematico della Università di Padova
Vdovin, E.P. (2006)
Sibirskij Matematicheskij Zhurnal
Ruifang Chen, Lujun Guo (2022)
Czechoslovak Mathematical Journal
Let be a normal subgroup of a group . The structure of is given when the -conjugacy class sizes of is a set of a special kind. In fact, we give the structure of a normal subgroup under the assumption that the set of -conjugacy class sizes of is , where , and are distinct primes for , .
Yahya Ould Hamidoune, Oriol Serra, Gilles Zémor (2006)
Acta Arithmetica
Kuznetsov, A.A. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Grechkoseeva, M.A. (2007)
Sibirskij Matematicheskij Zhurnal
Smith, Jonathan D.H. (2003)
Beiträge zur Algebra und Geometrie
Erika Damian, Andrea Lucchini (2006)
Rendiconti del Seminario Matematico della Università di Padova
van der Waall, Robert W., de Nijs, Cynthia H.W.M. (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
Zvonimir Janko (1976/1977)
Séminaire Bourbaki