3 citations · 5 across the 13 of their papers we have counts for
15 papers
The average element order and the number of conjugacy classes of finite groups
E. I. Khukhro, A. Moretó, M. Zarrin
Let be the average order of the elements of , where is a finite group. We show that there is no polynomial lower bound for in terms of , where $N\triangl…
A classification of the finite non-solvable minimal non-CA-groups
L. Jafari, S. Kohl, M. Zarrin
A group is called a CA-group if the centralizer of every non-central element is abelian. Furthermore, a group is called a minimal non-CA-group if it is not a CA-group itself, but a…
An affirmative answer to the Jainkin-Zapirain's question
M. Zarrin
If X is a non-empty subset of a finite group G, we denote by o(x) the order of x in G. Then we put The number o(X) is called the average order of X. Zapirain in 2011 , posed the fo…
groups with the same number of centralizers
K. Khoramshahi, M. Zarrin
For any group , let denote the set of all nonabelian centralizers of . Amiri and Rostami in (Publ. Math. Debrecen 87/3-4 (2015), 429-437) put forward the followin…
Criteria for nilpotency of groups via partitons
L. J. Taghvasani, M. Zarrin
Let be a finite group and . A cover for a group is a collection of subgroups of whose union is . We use the term -cover for a cover with members. A cove…
A counterexample to Herzog's Conjecture on the number of involutions
Mohammad Zarrin
In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this co…