Braces are generalizations of radical rings, introduced by Rump to study involutive non-
degenerate set-theoretical solutions of the Yang–Baxter equation (YBE). Skew braces were …

For a finite group G, let ψ (G) denote the sum of element orders of G. It is known that the
maximum value of ψ on the set of groups of order n, where n is a positive integer, will occur …

Comments are made on the following question. Let m, n be positive integers and ga finite
group. Suppose that for all choices of a subset of cardinality m and of a subset of cardinality …

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at
the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important …

For Γ a group of order mp, where p is a prime with gcd (p, m)= 1, we consider the regular
subgroups N≤ Perm (Γ) that are normalized by λ (Γ), the left regular representation of Γ …

In this article, we determine the structure of all nonabelian groups G such that G has the
minimum number of the element centralizers amongnonabelian groups of the same order …

For more than 100 years, group and number theorists have been interested in quesitons
such as:(a) If a group G has order| G|=∏ pi α i (pi distinct primes), what conditions on the …

ALMOST ABELIAN NUMBERS Page 1 Bull. Aust. Math. Soc. (First published online 2024),
page 1 of 6 ∗ doi:10.1017/S0004972724001126 ∗ Provisional—final page numbers to be …

A subgroup H of a group G is a solitary subgroup of G if G does not contain another
isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable …

Following Hujdurović et al.(2016), an automorphism of a graph is said to be even/odd if it
acts on the vertex set of the graph as an even/odd permutation. In this paper the formula for …