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- Title
Pronormality and Strong Pronormality of Subgroups.
- Authors
Vdovin, E.; Revin, D.
- Abstract
A subgroup H of a group G is said to be pronormal if, for any element g ∈ G, subgroups H and H are conjugate in $$ \left\langle {H,{H^g}} \right\rangle $$. A subgroup H of a group G is said to be strongly pronormal if, for any subgroup K ≤ H and any element g ∈ G, there exists an element $$ x\in \left\langle {H,{K^g}} \right\rangle $$ such that K ≤ H. Many known examples of pronormal subgroups, namely, normal subgroups, maximal subgroups, Sylow subgroups of finite groups, and Hall subgroups of finite soluble groups, will also exemplify strongly pronormal subgroups. It is shown that Carter subgroups of finite groups (which are always pronormal) are not strongly pronormal in general, even in soluble groups.
- Subjects
FINITE groups; SYLOW subgroups; GROUP theory; ABSTRACT algebra; ALGEBRA
- Publication
Algebra & Logic, 2013, Vol 52, Issue 1, p15
- ISSN
0002-5232
- Publication type
Article
- DOI
10.1007/s10469-013-9215-z