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POSET-BLOWDOWNS OF GENERALIZED QUATERNION GROUPS.
- Source :
- International Journal of Group Theory; Jun2024, Vol. 13 Issue 2, p133-160, 28p
- Publication Year :
- 2024
-
Abstract
- Poset-blowdown of subgroup posets of groups is an analog of blowdown in algebraic geometry. It is a poset map obtained by contracting normal subgroups. For finite groups, this is considered as a map between the Hasse diagrams of the subgroup posets. Poset-blowdowns are classified into three types: tame, wild, and hybrid depending on the sizes of their fibers. In this paper we describe the poset-blowdowns for generalized quaternion groups Q<subscript>2n</subscript> (n ≥ 3). They have distinguished nature in that all types (tame, wild, and hybrid) appear in the successive poset-blowdowns associated with the three chief series of Q<subscript>2n</subscript>. [ABSTRACT FROM AUTHOR]
- Subjects :
- QUATERNIONS
ALGEBRAIC geometry
FINITE groups
PARTIALLY ordered sets
Subjects
Details
- Language :
- English
- ISSN :
- 22517650
- Volume :
- 13
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- International Journal of Group Theory
- Publication Type :
- Academic Journal
- Accession number :
- 174769907
- Full Text :
- https://doi.org/10.22108/ijgt.2023.137628.1841