Groups Generated by a Class of Elements of Order 3.

Aschbacher, Michael; Hall, Marshall

doi:10.1016/s0304-0208(08)71820-6

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Introduction3

Le£ G Be Locally D-simple and δ A G Invariant Subset Of D1

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1973

2012

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Cited by 6 publications

(10 citation statements)

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“…The classification for p = 2 appears in [3]. The classification for p = 3 is incomplete, but a partial solution appears in [4] For the most part the proof here mimics that in the papers mentioned above. The exception comes in handling certain degenerate cases.…”

mentioning

confidence: 83%

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A characterization of the unitary and symplectic groups over finite fields of characteristic at least 5

Aschbacher¹

1973

Pacific J. Math.

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mentioning

confidence: 83%

“…Finally let β be a set of imprimitivity for Lemmas 2.6 and 2.7 are from §2 of [4]. 2.6 is a slight generalization of its counterpart, but the same proof goes through.…”

Section: Le£ G Be Locally D-simple and δ A G Invariant Subset Of Dmentioning

confidence: 99%

A characterization of the unitary and symplectic groups over finite fields of characteristic at least 5

Aschbacher¹

1973

Pacific J. Math.

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“…Surprisingly, during our calculations we never met any examples of Nichols algebras which satisfy our assumption but are not known to be finite-dimensional. Although there exist many indecomposable braided racks, for example, conjugacy classes of 3-transpositions, we do not use difficult classification results such as the classification of 3-transposition groups [Fis71], or [AH73].…”

Section: Introductionmentioning

confidence: 99%

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

Heckenberger

Lochmann

Vendramin

2012

Transformation Groups

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We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.

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“…The finite groups with similar properties were studied in [1,2] and used, for instance, in [3] for investigating the quadratic pairs for the prime number 3. As shown in [4], locally finite is each group G generated by a conjugacy class X of order 3 elements such that each noncommuting pair of elements of X generates a subgroup that is isomorphic to the alternating group of degree 4 or 5.…”

Section: Introductionmentioning

confidence: 99%