A note on involutive bases of Sylow 2-subgroups of symmetric groups

• Autorzy: Pawlik B.
• Języki publikacji: EN

Abstrakty

EN

The involutive base of a Sylow 2-subgroup Pn(2) of symmetric group S2n is a minimal generating set of this subgroup consisting of elements which are involutions. The Cayley graphs of group Pn(2) on involutive bases may be naturally considered as the undirected ones. The exact number of such bases is not known. In presented paper the necessary condition for base B of group Pn(2) to be involutive is prooved.

Słowa kluczowe

EN

Sylow p-subgroup; group base; wreath product of groups

PL

p-podgrupa Sylowa; baza grupy; splot grup

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2018
• Tom: Vol. 8, iss. 1
• Strony: 57--64
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pawlik B.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

• 1. Bier A., Sushchansky V.: Kaluzhnins representations of Sylow p-subgroups of automorphism groups of p-adic rooted trees. Algebra Discrete Math. 19, no. 1 (2015), 19–38.
• 2. Dixon J., Mortimer B.: Permutation Groups, Springer-Verlag, New York 1996.
• 3. Dmitruk Ju.V.: The structure of a Sylow 2-subgroup of the symmetric group of degree 2n. Ukr. Math. Zhurn. 30, no. 2 (1978), 155–164 (in Russian).
• 4. Kaluzhnin L.: Sur les p-group de Sylow du groupe symetricque du degree pm. C.R. Acad. Sci. Paris 221 (1945), 222–224 (in French).
• 5. Kaluzhnin L.: La structure des p-groupes de Sylow des groupes symetriques finis. Ann. Sci. L’Ecole Norm. Sup. 65 (1948), 239–272 (in French).
• 6. Pawlik B.: The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs. Algebra Discrete Math. 21, no. 2 (2016), 264–281.
• 7. Pawlik B.: The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups S2n on diagonal bases (under review).
• 8. Slupik A.J., Sushchansky V.I.: Minimal generating sets and Cayley graphs of Sylow p-subgroups of finite symmetric groups. Algebra Discrete Math. 8, no. 4 (2009), 167–184.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).