Add to ORKGIn this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset of the centralizer of an involution in a finite non-abelian simple group $G$ contains an odd order element, unless $G=\text{PSL}(n,2)$ for $n\geq 4$. More precisely, we show that the conjecture does not hold for the alternating group $A_{8n}$ for all $n\geq 2$
In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition,...
We consider the question of the determination of subgroups A and B such that A∩Bg ≠ 1 for any g ∈ G ...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135601/1/plms0052.pd
summary:Let $G$ be a finite group, and let $N(G)$ be the set of conjugacy class sizes of $G$. By Tho...
AbstractOrder components of a finite group are introduced in Chen (J. Algebra 15 (1996) 184). We pro...
In two previous papers we established the structure of the normal closure of a cyclic permutable sub...
L. Fuchs and S. Golomb considered the following problem. In a finite group G of order n, let p(G) de...
The authors describe the structure of the normal closure of a cyclic permutable subgroup of odd orde...
AbstractRecently, Thompson [9] constructed a new simple group E of order 215 ∘ 3105372 ∘ 13 ∘ 19 ∘ 3...
Abstract. There exist some characterizations about alternating and sym-metric groups. Some non-abeli...
AbstractLet An denote the alternating group on n symbols. If n = 5, 6, 7, 10, 11, 12, 13 or n ⩾ 15, ...
Eric Lander conjectured that if G is an abelian group of order $v$ containing a difference set of or...
This is the third and final installment of an exposition of an ACL2 formalization of finite group th...
Let G = A n, a finite alternating group. We study the commuting graph of G and establish, for all po...
AbstractAn automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. It was rec...
In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition,...
We consider the question of the determination of subgroups A and B such that A∩Bg ≠ 1 for any g ∈ G ...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135601/1/plms0052.pd
summary:Let $G$ be a finite group, and let $N(G)$ be the set of conjugacy class sizes of $G$. By Tho...
AbstractOrder components of a finite group are introduced in Chen (J. Algebra 15 (1996) 184). We pro...
In two previous papers we established the structure of the normal closure of a cyclic permutable sub...
L. Fuchs and S. Golomb considered the following problem. In a finite group G of order n, let p(G) de...
The authors describe the structure of the normal closure of a cyclic permutable subgroup of odd orde...
AbstractRecently, Thompson [9] constructed a new simple group E of order 215 ∘ 3105372 ∘ 13 ∘ 19 ∘ 3...
Abstract. There exist some characterizations about alternating and sym-metric groups. Some non-abeli...
AbstractLet An denote the alternating group on n symbols. If n = 5, 6, 7, 10, 11, 12, 13 or n ⩾ 15, ...
Eric Lander conjectured that if G is an abelian group of order $v$ containing a difference set of or...
This is the third and final installment of an exposition of an ACL2 formalization of finite group th...
Let G = A n, a finite alternating group. We study the commuting graph of G and establish, for all po...
AbstractAn automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. It was rec...
In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition,...
We consider the question of the determination of subgroups A and B such that A∩Bg ≠ 1 for any g ∈ G ...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135601/1/plms0052.pd