On central difference sets in certain non-abelian 2-groups

Rod Gow; Rachel Quinlan

doi:10.1016/j.jcta.2005.05.006

On central difference sets in certain non-abelian 2-groups

Rod Gow
, Rachel Quinlan

University College Dublin

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

3 Citations (Scopus)

Abstract

In this note, we define the class of finite groups of Suzuki type, which are non-abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with G = 2^2s always possesses a non-trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non-trivial central difference set.

Original language	English
Pages (from-to)	712-717
Number of pages	6
Journal	Journal of Combinatorial Theory. Series A
Volume	113
Issue number	4
DOIs	https://doi.org/10.1016/j.jcta.2005.05.006
Publication status	Published - May 2006
Externally published	Yes

Keywords

Central difference set
Conjugacy class
Non-abelian 2-group

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10.1016/j.jcta.2005.05.006

Cite this

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title = "On central difference sets in certain non-abelian 2-groups",

abstract = "In this note, we define the class of finite groups of Suzuki type, which are non-abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with G = 22s always possesses a non-trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non-trivial central difference set.",

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AU - Gow, Rod

AU - Quinlan, Rachel

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AB - In this note, we define the class of finite groups of Suzuki type, which are non-abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with G = 22s always possesses a non-trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non-trivial central difference set.

KW - Central difference set

KW - Conjugacy class

KW - Non-abelian 2-group

UR - https://www.scopus.com/pages/publications/33645543272

U2 - 10.1016/j.jcta.2005.05.006

DO - 10.1016/j.jcta.2005.05.006

M3 - Article

SN - 0097-3165

VL - 113

SP - 712

EP - 717

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 4

ER -

On central difference sets in certain non-abelian 2-groups

Abstract

Keywords

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