The nonexistence of projective planes of order 12 with a collineation group of order 8
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DOI: 10.1002/jcd.20175
Abstract: In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We… read more here.
Keywords: order; group order; nonexistence projective; collineation group ... See more keywords
Eparability of Schur Rings Over an Abelian Group of Order 4p
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DOI: 10.1007/s10958-019-04563-9
Abstract: An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\mathcal{K}$ if every its algebraic isomorphism to an $S$-ring over a group from $\mathcal{K}$ is induced by a… read more here.
Keywords: abelian group; group; schur rings; group order ... See more keywords
Information can explain the dynamics of group order in animal collective behaviour
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DOI: 10.1038/s41467-020-16578-x
Abstract: Animal groups vary in their collective order (or state), forming disordered swarms to highly polarized groups. One explanation for this variation is that individuals face differential benefits or costs depending on the group’s order, but… read more here.
Keywords: information; collective behaviour; group; social information ... See more keywords
Modular quotient varieties and singularities by the cyclic group of order 2p
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DOI: 10.1080/00927872.2020.1791148
Abstract: Abstract We classify all n-dimensional reduced Cohen-Macaulay modular quotient varieties and study their singularities, where p is a prime number and denotes the cyclic group of order 2p. In particular, we present an example that… read more here.
Keywords: cyclic group; modular quotient; group order; quotient varieties ... See more keywords
On two conjectures about the sum of element orders
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DOI: 10.4153/s0008439521000047
Abstract: Abstract Let G be a finite group and $\psi (G) = \sum _{g \in G} o(g)$ , where $o(g)$ denotes the order of $g \in G$ . There are many results on the influence of… read more here.
Keywords: two conjectures; psi; group order; conjectures sum ... See more keywords