arXiv subjects

L. Jafari Taghvasani

Publications and source records attributed to L. Jafari Taghvasani.

2 recordsLinked to original sources

arXiv2015

A characterization of A_5 by its Same-order type

Let G be a group, define an equivalence relation s as below: 8 g; h 2 G g s h () jgj = jhj the set of sizes of equivalence classes with respect to this relation is called the same-order type of G. Shen et al. (Monatsh. Math. 160 (2010), 337-341.), showed that A5 is the only group with the same-order type f1; 15; 20; 24g. In this paper, among other things, we prove that a nonabelian simple group G has same-order type fr; m; n; kg if and only if G ?= A5.

math.GR↗

arXiv2015

Shen's conjecture on groups with given same order type

For any group $G$, we define an equivalence relation $\thicksim$ as below: $$\forall \ g, h \in G \ \ g\thicksim h \Longleftrightarrow |g|=|h|$$ the set of sizes of equivalence classes with respect to this relation is called the same-order type of $G$ and denote by $α{(G)}$. In this paper, we give a partial answer to a conjecture raised by Shen. In fact, we show that if $G$ is a nilpotent group, then $|π(G)|\leq |α{(G)}|$, where $π(G)$ is the set of prime divisors of order of $G$. Also we investigate the groups all of whoseproper subgroups, say $H$ have $|α{(H)}|\leq 2$.

math.GR↗