On the extension of involutorial Bol loops

Kiechle, Hubert; Nagy, Gábor P.

doi:10.1007/bf02941674

Cited by 14 publications

(12 citation statements)

References 4 publications

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“…Later, many infinite classes of such loops were given; see [11,12,13,16]. All of these examples were solvable loops; equivalently the group G was a 2-group.…”

Section: Loop Q Is a (Right) Bol Loop If The Identity ((Xy)z)y = X(y(mentioning

confidence: 99%

“…In [12,Section 5] and [16,Theorem 5.5], the authors constructed rich classes of Bol loops of exponent 2 having the same enveloping groups, namely the wreath product C n 2 C 2 and the extra special 2-group E + 2 2n+1 , respectively. In these cases, a simple parametrization of the conjugacy classes of involutions enabled a description of the associated loops.…”

Section: Lemma 42 With the Notation Above We Have The Followingmentioning

confidence: 99%

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A class of finite simple Bol loops of exponent 2

Nagy

2009

Trans. Amer. Math. Soc.

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“…Later, many infinite classes of such loops were given; see [11,12,13,16]. All of these examples were solvable loops; equivalently the group G was a 2-group.…”

Section: Loop Q Is a (Right) Bol Loop If The Identity ((Xy)z)y = X(y(mentioning

confidence: 99%

Section: Lemma 42 With the Notation Above We Have The Followingmentioning

confidence: 99%

A class of finite simple Bol loops of exponent 2

Nagy

2009

Trans. Amer. Math. Soc.

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“…Some other papers dealing with LCC Bol loops are [17] and [14]. LCC loops Q which satisfy |Q : N λ | = 2 or |Q : N ρ | = 2 are considered in [9].…”

Section: Introductionmentioning

confidence: 99%

On extraspecial left conjugacy closed loops

Drápal

2006

Journal of Algebra

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A loop Q is said to be left conjugacy closed (LCC) if L x L y L −1x is a left translation for all x, y ∈ Q. We describe all LCC loops Q such that Q/Z is an elementary abelian p-group, where Z ¡ Q is a central subloop of order p. We single out those that are right conjugacy closed as well, and show their connection to trilinear mappings and quadratic forms. Isomorphism classes are determined for the case Z = Z(Q), i.e. for the extraspecial loops.

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“…There are many papers in the literature, among them [1,3,7,8,[11][12][13]15,17,[19][20][21][22][23][24][25]27] that describe methods of constructing Bol loops. In some of these, the Bol loop is constructed as a central extension of a group.…”

Section: Introductionmentioning

confidence: 99%

A new construction of Bol loops of order 8k

Chein

Goodaire

2005

Journal of Algebra

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One of the most interesting constructions of nonassociative Moufang loops is the construction by the first author of the loops M(G, 2) [Trans. Amer. Math. Soc. 188 (1974) 31-51], in which the new loop is constructed as a split extension of a nonabelian group G by a cyclic group of order 2. This same construction will not produce non-Moufang Bol loops, even if we start with a Moufang loop instead of a group. We generalize the construction to produce a large class of Bol loops as extensions of B by C m × C n , where B can be any group or even any loop which satisfies the right Bol identity. We determine conditions under which the newly constructed loops will be Moufang and when they will be associative. We also find the nuclei, centrum, centre, and commutator/associator subloop of a loop constructed by this method, and we investigate which known Bol loops of small orders arise in this way.  2005 Elsevier Inc. All rights reserved.

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On the extension of involutorial Bol loops

Cited by 14 publications

References 4 publications

A class of finite simple Bol loops of exponent 2

A class of finite simple Bol loops of exponent 2

On extraspecial left conjugacy closed loops

A new construction of Bol loops of order 8k

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