On association schemes all elements of which have valency 1 or 2

Mikhail Muzychuk; Paul Hermann Zieschang

doi:10.1016/j.disc.2007.08.035

On association schemes all elements of which have valency 1 or 2

Mikhail Muzychuk, Paul Hermann Zieschang

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In the present note, we investigate schemes S in which each element s satisfies n_s ≤ 2 and n_{s* s} ≠ 2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G // 〈 t 〉, where G is a finite group and t an involution of G weakly closed in C_G (t). Groups G with an involution t weakly closed in C_G (t) have been described in Glauberman's Z^*-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403-420] with the help of the largest normal subgroup of G having odd order.

Original language	English
Pages (from-to)	3097-3103
Number of pages	7
Journal	Discrete Mathematics
Volume	308
Issue number	14
DOIs	https://doi.org/10.1016/j.disc.2007.08.035
State	Published - 28 Jul 2008
Externally published	Yes

Keywords

Association scheme
Schurian
Weakly closed involution

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2007.08.035

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title = "On association schemes all elements of which have valency 1 or 2",

abstract = "In the present note, we investigate schemes S in which each element s satisfies ns ≤ 2 and ns* s ≠ 2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G // 〈 t 〉, where G is a finite group and t an involution of G weakly closed in CG (t). Groups G with an involution t weakly closed in CG (t) have been described in Glauberman's Z*-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403-420] with the help of the largest normal subgroup of G having odd order.",

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AU - Muzychuk, Mikhail

AU - Zieschang, Paul Hermann

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N2 - In the present note, we investigate schemes S in which each element s satisfies ns ≤ 2 and ns* s ≠ 2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G // 〈 t 〉, where G is a finite group and t an involution of G weakly closed in CG (t). Groups G with an involution t weakly closed in CG (t) have been described in Glauberman's Z*-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403-420] with the help of the largest normal subgroup of G having odd order.

AB - In the present note, we investigate schemes S in which each element s satisfies ns ≤ 2 and ns* s ≠ 2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G // 〈 t 〉, where G is a finite group and t an involution of G weakly closed in CG (t). Groups G with an involution t weakly closed in CG (t) have been described in Glauberman's Z*-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403-420] with the help of the largest normal subgroup of G having odd order.

KW - Association scheme

KW - Schurian

KW - Weakly closed involution

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DO - 10.1016/j.disc.2007.08.035

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SP - 3097

EP - 3103

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 14

ER -

On association schemes all elements of which have valency 1 or 2

Abstract

Keywords

ASJC Scopus subject areas

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