THE PROBABILITY OF COMMUTING SUBGROUPS IN ARBITRARY LATTICES OF SUBGROUPS

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Muhie Seid Kassaw; Russo Francesco G.

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2021 | Volume:10 | Issue:3 Page(s): 125-135

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Title

THE PROBABILITY OF COMMUTING SUBGROUPS IN ARBITRARY LATTICES OF SUBGROUPS

Author(s)

Muhie Seid Kassaw | Russo Francesco G. | Issue Writer Certificate

Keywords

Subgroup commutativity degree

Dihedral groups

Sublattices

Elementary abelian p-groups

polynomial functions

Abstract

A , nite group G, in which two randomly chosen subgroups H and K commute, has been classi, ed by Iwasawa in 1941. It is possible to de, ne a probabilistic notion, which \measures the distance" of G from the groups of Iwasawa. Here we introduce the generalized Subgroup commutativity degree gsd(G) for two arbitrary Sublattices S(G) and T(G) of the lattice of subgroups L(G) of G. Upper and lower bounds for gsd(G) are shown and we study the behaviour of gsd(G) with respect to subgroups and quotients, showing new numerical restrictions.

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APA: Copy

Muhie, Seid Kassaw, & Russo, Francesco G.. (2021). THE PROBABILITY OF COMMUTING SUBGROUPS IN ARBITRARY LATTICES OF SUBGROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 10(3), 125-135. SID. https://sid.ir/paper/1004108/en

Vancouver: Copy

Muhie Seid Kassaw, Russo Francesco G.. THE PROBABILITY OF COMMUTING SUBGROUPS IN ARBITRARY LATTICES OF SUBGROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2021;10(3):125-135. Available from: https://sid.ir/paper/1004108/en

IEEE: Copy

Seid Kassaw Muhie, and Francesco G. Russo, “THE PROBABILITY OF COMMUTING SUBGROUPS IN ARBITRARY LATTICES OF SUBGROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 10, no. 3, pp. 125–135, 2021, [Online]. Available: https://sid.ir/paper/1004108/en

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