Results 1 to 10 of about 1,309 (212)
Cryptanalysis of some nonabelian group-based key exchange protocols [PDF]
Journal of Mathematical CryptologyIn the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the conjugacy search problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper, we discuss the
Tinani Simran +2 more
doaj +2 more sources
Linear Groups with Restricted Conjugacy Classes [PDF]
Ricerche di Matematica, 2021 AbstractIn this paper we characterize, in terms of their conjugacy classes, linear groups G such that $$G/\zeta _k(G)$$ G / ζ k ( G
de Giovanni F. +2 more
openaire +5 more sources
Powers of conjugacy classes in a finite group [PDF]
Annali Di Matematica Pura Ed Applicata, 2019 The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes.
Antonio Beltran +2 more
exaly +8 more sources
On conjugacy classes in groups
Journal of AlgebraLet $G$ be a group. Write $G^{*}=G\setminus \{1\}$. An element $x$ of $G^{*}$ will be called deficient if $ \langle x\rangle < C_G(x)$ and it will be called non-deficient if $\langle x\rangle = C_G(x).$ If $x\in G$ is deficient (non-deficient), then the conjugacy class $x^G$ of $x$ in $G$ will be also called deficient (non-deficient).
Marcel Herzog +2 more
exaly +5 more sources
On the number of conjugacy classes of a permutation group
Journal of Combinatorial Theory - Series A, 2015 We prove that any permutation group of degree $n \geq 4$ has at most $5^{(n-1)/3}$ conjugacy classes.
Martino Garonzi, Attila Maroti
exaly +5 more sources
New lower bounds for the number of conjugacy classes in finite nilpotent groups [PDF]
International Journal of Group Theory, 2022 P. Hall's classical equality for the number of conjugacy classes in $p$-groups yields $k(G) \ge (3/2) \log_2 |G|$ when $G$ is nilpotent. Using only Hall's theorem, this is the best one can do when $|G| = 2^n$. Using a result of G.J.
Edward A. Bertram
doaj +1 more source
Conjugacy classes contained in normal subgroups: an overview [PDF]
International Journal of Group Theory, 2018 We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group.
Antonio Beltran +2 more
doaj +1 more source
Groups with Černikov conjugacy classes [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1991 AbstractThe aim of this paper is to prove some embedding theorems for groups with Černikov conjugacy classes. Moreover a characterization of periodic central-by-Černikov groups is given.
DE GIOVANNI, FRANCESCO +2 more
openaire +3 more sources
On the Regular Power Graph on the Conjugacy Classes of Finite Groups [PDF]
Mathematics Interdisciplinary Research, 2018 The (undirected) power graph on the conjugacy classes PC(G) of a group G is a simple graph in which the vertices are the conjugacy classes of G and two distinct vertices C and C' are adjacent in PC(G) if one is a subset of a power of the other.
Sajjad Mahmood Robati
doaj +1 more source
Symmetric groups and conjugacy classes [PDF]
Journal of Group Theory, 2008 Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial $α,β\in S_n$, we prove that the product $α^{S_n}β^{S_n}$ of the conjugacy classes $α^{S_n}$ and $β^{S_n}$ is never a conjugacy class. Furthermore, if n is not even and $n$ is not a multiple of three, then $α^{S_n}β^{S_n}$ is the union of at least three distinct conjugacy ...
Adan-Bante, Edith, Verrill, Helena
openaire +3 more sources