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We prove that if the average number of Sylow subgroups of a finite group is less than $\frac{41}{5}$ and not equal to $\frac{29}{4}$ , then $G$ is solvable or $G / F (G) ≅ A_{5}$ . In particular, if the average number of Sylow subgroups of a finite group is $\frac{29}{4}$ , then $G / N ≅ A_{5}$ , where $N$ is the largest normal solvable subgroup of $G$ . This generalizes an earlier result by Moretó et al.

On the Breadth of a Finite p-Group.

Joseph A. Gallian (1972)

Mathematische Zeitschrift

On the centralizer of an automorphism of order 2 of the Burnside group $B_{0} (2, 5)$ .

Kuznetsov, A.A., Filippov, K.A. (2010)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

On the cohomology of groups of p-length 1.

Thomas Diethelm (1983)

Commentarii mathematici Helvetici

On the commutator lengths of certain classes of finitely presented groups.

Doostie, H., Campbell, P.P. (2006)

International Journal of Mathematics and Mathematical Sciences

On the composition factors of a group with the same prime graph as $B_{n} (5)$

Azam Babai, Behrooz Khosravi (2012)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. The prime graph of $G$ is a graph whose vertex set is the set of prime divisors of $| G |$ and two distinct primes $p$ and $q$ are joined by an edge, whenever $G$ contains an element of order $p q$ . The prime graph of $G$ is denoted by $Γ (G)$ . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if $G$ is a finite group such that $Γ (G) = Γ (B_{n} (5))$ , where $n \geq 6$ , then $G$ has a unique nonabelian composition factor isomorphic to $B_{n} (5)$ or $C_{n} (5)$ .

On the computation of the order of Janko’s first simple group $𝔉_{1}$

Herbert Dietzsch (1971)

Rendiconti del Seminario Matematico della Università di Padova

On the conjugacy problem for Carter subgroups.

Vdovin, E.P. (2006)

Sibirskij Matematicheskij Zhurnal

On the conjugate type vector and the structure of a normal subgroup

Ruifang Chen, Lujun Guo (2022)

Czechoslovak Mathematical Journal

Let $N$ be a normal subgroup of a group $G$ . The structure of $N$ is given when the $G$ -conjugacy class sizes of $N$ is a set of a special kind. In fact, we give the structure of a normal subgroup $N$ under the assumption that the set of $G$ -conjugacy class sizes of $N$ is $(p_{1 n_{1}}^{a_{1 n_{1}}}, \dots, p_{11}^{a_{11}}, 1) \times \dots \times (p_{r n_{r}}^{a_{r n_{r}}}, \dots, p_{r 1}^{a_{r 1}}, 1)$ , where $r > 1$ , $n_{i} > 1$ and $p_{i j}$ are distinct primes for $i \in {1, 2, \dots, r}$ , $j \in {1, 2, \dots, n_{i}}$ .

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Displaying 661 – 680 of 1356

On (t + ...)-transitive Permutation Groups.

On the Additive Groups of Finite Near Integral Domains and Simple d.g. Near Rings.

On the algebraic form of Keller's conjecture

On the automorphism of a class of groups.

On the average number of Sylow subgroups in finite groups

On the Breadth of a Finite p-Group.

On the centralizer of an automorphism of order 2 of the Burnside group $B_{0} (2, 5)$ .

On the cohomology of groups of p-length 1.

On the commutator lengths of certain classes of finitely presented groups.

On the composition factors of a group with the same prime graph as $B_{n} (5)$

On the computation of the order of Janko’s first simple group $𝔉_{1}$

On the conjugacy problem for Carter subgroups.

On the conjugate type vector and the structure of a normal subgroup

On the critical pair theory in ℤ/pℤ

On the definability of the group $L_{2} (7)$ by its spectrum.

On the difference between the spectra of the simple groups $B_{n} (q)$ and $C_{n} (q)$ .

On the dimension of finite permutation group actions.

On the Dirichlet polynomial of finite group of Lie type

On the embedding of a finite group as Frattini subgroup.

On the finite simple groups

Currently displaying 661 – 680 of 1356