A CLASSIFICATION OF NILPOTENT 3-BCI GROUPS

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KOIKE HIROKI; KOVACS ISTVAN

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Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2019 | Volume:8 | Issue:2 Page(s): 11-24

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Title

A CLASSIFICATION OF NILPOTENT 3-BCI GROUPS

Author(s)

KOIKE HIROKI | KOVACS ISTVAN | Issue Writer Certificate

Keywords

bi-Cayley graph

BCI-group

graph isomorphism

Abstract

Given a finite group G and a subset S G; the bi-Cayley graph BCay(G; S) is the graph whose vertex set is G f0; 1g and edge set is ff(x; 0); (sx; 1)g: x 2 G; s 2 Sg. A bi-Cayley graph BCay(G; S) is called a BCI-graph if for any bi-Cayley graph BCay(G; T); BCay(G; S) =B C a y ( G; T ) implies that T = gS for some g 2 G and 2 Aut(G). A group G is called an m-BCI-group if all bi-Cayley graphs of G of valency at most m are BCI-graphs. It was proved by Jin and Liu that, if G is a 3-BCI-group, then its Sylow 2-subgroup is cyclic, or elementary abelian, or Q8 [European J. Combin. 31 (2010) 1257{1264], and that a Sylow p-subgroup, p is an odd prime, is homocyclic [Util. Math. 86 (2011) 313{320]. In this paper we show that the converse also holds in the case when G is nilpotent, and hence complete the classification of nilpotent 3-BCI-groups.

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APA: Copy

KOIKE, HIROKI, & KOVACS, ISTVAN. (2019). A CLASSIFICATION OF NILPOTENT 3-BCI GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 8(2), 11-24. SID. https://sid.ir/paper/723593/en

Vancouver: Copy

KOIKE HIROKI, KOVACS ISTVAN. A CLASSIFICATION OF NILPOTENT 3-BCI GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2019;8(2):11-24. Available from: https://sid.ir/paper/723593/en

IEEE: Copy

HIROKI KOIKE, and ISTVAN KOVACS, “A CLASSIFICATION OF NILPOTENT 3-BCI GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 8, no. 2, pp. 11–24, 2019, [Online]. Available: https://sid.ir/paper/723593/en

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