DOI: 10.12732/ijam.v38i2.2
COUNTEREXAMPLES FOR SOME CONJECTURES
OF FINITE GROUPS
Ibrahim A. Jawarneh 1, Bilal N. Al-Hasanat 2,§
Department of Mathematics
Al Hussein Bin Talal University
Ma’an, JORDAN
Abstract. For a finite group G, let $\pi_e(G)$ be the set of orders of its elements.
The order classes of G, denoted as OC(G), are collections of pairs [k,m], where $k \in \pi_e (G)$
and m represents the number of elements in G with order k. Two finite groups G and H are said to be of the same order type if OC(G) = OC(H). It is unequivocal that two simple groups G1 and
G2 with the same order classes are isomorphic. This paper presents counterexamples
demonstrating that this property does not necessarily hold for non-simple groups. Furthermore, we will examine several properties of non-simple groups that derived from their group order and element orders, and address certain open problems related to these properties.
How
to cite this paper?
DOI: 10.12732/ijam.v38i2.2
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
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