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Splitting via Noncommutativity. / Lewis, Mark Lanning; Lytkina, Daria; Mazurov, Viktor Danilovich et al.

In: Taiwanese Journal of Mathematics, Vol. 22, No. 5, 01.10.2018, p. 1051-1082.

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

Harvard

Lewis, ML, Lytkina, D, Mazurov, VD & Moghaddamfar, AR 2018, 'Splitting via Noncommutativity', Taiwanese Journal of Mathematics, vol. 22, no. 5, pp. 1051-1082. https://doi.org/10.11650/tjm/180202

APA

Lewis, M. L., Lytkina, D., Mazurov, V. D., & Moghaddamfar, A. R. (2018). Splitting via Noncommutativity. Taiwanese Journal of Mathematics, 22(5), 1051-1082. https://doi.org/10.11650/tjm/180202

Vancouver

Lewis ML, Lytkina D, Mazurov VD, Moghaddamfar AR. Splitting via Noncommutativity. Taiwanese Journal of Mathematics. 2018 Oct 1;22(5):1051-1082. doi: 10.11650/tjm/180202

Author

Lewis, Mark Lanning ; Lytkina, Daria ; Mazurov, Viktor Danilovich et al. / Splitting via Noncommutativity. In: Taiwanese Journal of Mathematics. 2018 ; Vol. 22, No. 5. pp. 1051-1082.

BibTeX

@article{31d297a768ff48119a1f7796252b428d,
title = "Splitting via Noncommutativity",
abstract = "Let G be a nonabelian group and n a natural number. We say that G has a strict n-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup A and n nonempty subsets B-1, B-2, . . . , B-n, such that vertical bar B-i vertical bar > 1 for each i and within each set B-i, no two distinct elements commute. We show that every finite nonabelian group has a strict n-split decomposition for some n. We classify all finite groups G, up to isomorphism, which have a strict n-split decomposition for n = 1, 2, 3. Finally, we show that for a nonabelian group G having a strict n-split decomposition, the index vertical bar G : A vertical bar is bounded by some function of n.",
keywords = "strict n-split decomposition, simple group, commuting graph, Commuting graph, Simple group, Strict n-split decomposition",
author = "Lewis, {Mark Lanning} and Daria Lytkina and Mazurov, {Viktor Danilovich} and Moghaddamfar, {Ali Reza}",
year = "2018",
month = oct,
day = "1",
doi = "10.11650/tjm/180202",
language = "English",
volume = "22",
pages = "1051--1082",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "MATHEMATICAL SOC REP CHINA",
number = "5",

}

RIS

TY - JOUR

T1 - Splitting via Noncommutativity

AU - Lewis, Mark Lanning

AU - Lytkina, Daria

AU - Mazurov, Viktor Danilovich

AU - Moghaddamfar, Ali Reza

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Let G be a nonabelian group and n a natural number. We say that G has a strict n-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup A and n nonempty subsets B-1, B-2, . . . , B-n, such that vertical bar B-i vertical bar > 1 for each i and within each set B-i, no two distinct elements commute. We show that every finite nonabelian group has a strict n-split decomposition for some n. We classify all finite groups G, up to isomorphism, which have a strict n-split decomposition for n = 1, 2, 3. Finally, we show that for a nonabelian group G having a strict n-split decomposition, the index vertical bar G : A vertical bar is bounded by some function of n.

AB - Let G be a nonabelian group and n a natural number. We say that G has a strict n-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup A and n nonempty subsets B-1, B-2, . . . , B-n, such that vertical bar B-i vertical bar > 1 for each i and within each set B-i, no two distinct elements commute. We show that every finite nonabelian group has a strict n-split decomposition for some n. We classify all finite groups G, up to isomorphism, which have a strict n-split decomposition for n = 1, 2, 3. Finally, we show that for a nonabelian group G having a strict n-split decomposition, the index vertical bar G : A vertical bar is bounded by some function of n.

KW - strict n-split decomposition

KW - simple group

KW - commuting graph

KW - Commuting graph

KW - Simple group

KW - Strict n-split decomposition

UR - http://www.scopus.com/inward/record.url?scp=85060093296&partnerID=8YFLogxK

U2 - 10.11650/tjm/180202

DO - 10.11650/tjm/180202

M3 - Article

VL - 22

SP - 1051

EP - 1082

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 5

ER -

ID: 18641848