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The paper reports the results of a search for pairs of groups of order $n$ that can be placed in the distance $n^{2} / 4$ for the case when $n \in {16, 32}$ . The constructions that are used are of the general character and some of their properties are discussed as well.

On sM-group.

How, Guan Aun (2003)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On supersoluble groups acting on Klein surfaces.

Grzegorz Gromadzki (1990)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

On the algebraic form of Keller's conjecture

K. Corrádi, S. Szabó (1990)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

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 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 161 – 180 of 320

On recognition by spectrum of finite simple linear groups over fields of characteristic 2.

On recognition of all finite nonabelian simple groups with orders having prime divisors at most 13.

On recognition of finite simple groups with connected prime graph.

On recognition of the finite simple orthogonal groups of dimension $2^{m}$ , $2^{m} + 1$ , and $2^{m} + 2$ over a field of characteristic 2.

On recognition of the projective special linear groups over binary fields.

On small distances of small 2-groups

On sM-group.

On supersoluble groups acting on Klein surfaces.

On the algebraic form of Keller's conjecture

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 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 influence of the indices of normalizers of Sylow subgroups on the structure of a finite $p$ -soluble group.

On the largest conjugacy class size in a finite group

On the noncommuting graph associated with a finite group.

On the number of conjugacy classes in a finite group

On the number of conjugacy classes of pi-elements in a finite group

Currently displaying 161 – 180 of 320