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Elementary abelian $$\varvec{p}$$p-groups are the only finite groups with the Borsuk–Ulam property

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1 Published in 2019 at "Journal of Fixed Point Theory and Applications"

DOI: 10.1007/s11784-018-0654-y

Abstract: It is well known that the Borsuk–Ulam theorem holds for elementary abelian p-groups $$C_p{}^k$$Cpk. When the Borsuk–Ulam theorem holds for a finite group G, we say that G has the Borsuk–Ulam property or G is… read more here.

Keywords: elementary abelian; finite groups; borsuk ulam; ulam property ... See more keywords

Bent Partitions and LP-Packings

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0 Published in 2024 at "IEEE Transactions on Information Theory"

DOI: 10.1109/tit.2024.3359260

Abstract: Recently, the concept of (normal) bent partitions, which are partitions of elementary abelian groups having similar properties to spreads, has been introduced by Anbar and Meidl. A large number of bent partitions, so-called generalized semifield… read more here.

Keywords: elementary abelian; abelian groups; bent partitions; semifield spreads ... See more keywords

Skew-morphisms of elementary abelian 𝑝-groups

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0 Published in 2024 at "Journal of Group Theory"

DOI: 10.1515/jgth-2022-0092

Abstract: Abstract A skew-morphism of a finite group 𝐺 is a permutation 𝜎 on 𝐺 fixing the identity element, and for which there exists an integer-valued function 𝜋 on 𝐺 such that σ ⁢ ( x… read more here.

Keywords: elementary abelian; mathbb; skew morphisms; sigma ... See more keywords