On the isotopic characterizations of generalized Bol loops

Adeniran, John Olushola; Jaiyeola, Temitope Gbolahan; Ìdòwú, K. A.

doi:10.22199/issn.0717-6279-4581

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…In (Adeniran et al [2], 2015) carried out a study of some isotopic characterisation of generalised Bol loops. In (Jaiyéo .…”

Section: Middle Bol Loopmentioning

confidence: 99%

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Crypto-automorphism group of some quasigroups

Oyebo¹,

Osoba²,

Jaiyeola³

2024

Discuss. Math. - General Algebra and Applications

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In quasigroup and loop theory, a pseudo-automorphism (with single companion) is known to generalize automorphism. In this work, the set of crypto-automorphisms (with twin companion) of a quasigroup with right and left identity elements were shown to form a group. For a quasigroup with right and left identity elements, some results on autotopic characterizations of crypto-automorphisms were established and used to deduce some subgroups of the crypto-automorphism group of a middle Bol loop. The crypto-automorphism group and Bryant-Schneider group (this has been used in the study of the isotopy-isomorphy of some varieties of loops e.g. Bol loops, Moufang loops, Osborn loops) of a loop were found to coincide.

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“…In (Adeniran et al [2], 2015) carried out a study of some isotopic characterisation of generalised Bol loops. In (Jaiyéo .…”

Section: Middle Bol Loopmentioning

confidence: 99%

“…lá et al [18], 2017) studied the holomorphic structure of middle Bol loops and showed that the holomorph of a commutative loop is commutative middle Bol loop if and only if the loop is a middle Bol loop and its automorphism group is abelian. Adeniran et al [3,4], Jaiyéo . lá and Popoola [28] studied generalised Bol loops.…”

Section: Middle Bol Loopmentioning

confidence: 99%

Crypto-automorphism group of some quasigroups

Oyebo¹,

Osoba²,

Jaiyeola³

2024

Discuss. Math. - General Algebra and Applications

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“…In 2015, Adeniran et al [6] carried out a study of some isotopic characterisation of generalised Bol loops. In 2017, Jaiyéo .…”

Section: Introductionmentioning

confidence: 99%

“…lá et al [23] studied the holomorphic structure of middle Bol loops and showed that the holomorph of a commutative loop is a commutative middle Bol loop if and only if the loop is a middle Bol loop and its automorphism group is abelian. Adeniran et al [7,8], Jaiyéo . lá and Popoola [29] studied generalised Bol loops.…”

Section: Introductionmentioning

confidence: 99%

Isostrophy Bryant-Schneider Group-Invariant of Bol Loops

Jaíyéolá¹,

Osoba²,

Oyem³

2023

BASM

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In the recent past, Grecu and Syrbu (in no order of preference) have jointly and individually reported some results on isostrophy invariants of Bol loops. Also, the Bryant-Schneider group of a loop has been found important in the study of the isotopy-isomorphy of some varieties of loops (e.g. Bol loops, Moufang loops, Osborn loops). In this current work, the Bryant-Schneider group of a middle Bol loop was linked with some of the isostrophy-group invariance results of Grecu and Syrbu. In particular, it was shown that some subgroups of the Bryant-Schneider group of a middle Bol loop are equal (or isomorphic) to the automorphism and pseudo-aumorphism groups of its corresponding right (left) Bol loop. Some elements of the Bryant-Schneider group of a middle Bol loop were shown to induce automorphisms and middle pseudo-automorphisms. It was discovered that if a middle Bol loop is of exponent 2, then, its corresponding right (left) Bol loop is a left (right) G-loop.

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