1. On Auto-Engle groups and Auto-Bell groups.
- Author
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Rostamyari, Mohammad Amin, Mousavi, Azam K., and Moghaddam, Mohammad Reza R.
- Subjects
- *
GROUP theory , *NILPOTENT groups , *MATHEMATICAL bounds , *ABELIAN groups , *AUTOMORPHISMS - Abstract
The third author et al. in 2013, introduced and studied the concept of auto-Bell groups. A group G is said to be n-auto-Bell if [xn, α] = [x, αn], for all x in G, α in Aut(G) and any integer n ≠ 0, 1. Let Ln(G) be the nth-absolute centre of the group G, then some sharp bounds for the exponents of G/L2(G) and G/L3 (G) are constructed, when G is an n-auto-Bell abelian or n-auto-Bell groups. Finally, we show that <øx, α> is nilpotent of class at most 4, for every inner automorphism øx induced by an element x of G and α in Aut(G), when G is a 3-auto-Engel group. [ABSTRACT FROM AUTHOR]
- Published
- 2015