A note on locally soluble almost subnormal subgroups in divsion rings

نویسندگان
Behravesh, Hoshang ID 1
Ghaffarzadeh, Mehdi ID 2
Ghasemi, Mohsen ID 3
Hekmatara, Somayeh ID 4

1 Department of Mathematics, Urmia University, Urmia , Iran

2 Department of Mathematics, Khoy Branch, Islamic Azad University, Khoy , Iran

3 Department of Mathematics, Urmia University, Urmia , Iran

4 Department of Mathematics, Urmia University, Urmia , Iran

doi
10.22108/ijgt.2019.116399.1546
چکیده

Let $D$ be a division ring with center $F$ and assume that $N$ is a locally soluble almost subnormal subgroup of the multiplicative group $D^*$ of $D$‎. ‎We prove that if $N$ is algebraic over $F$‎, ‎then $N$ is central‎. ‎This answers partially \cite[Conjecture 1]{hai_13}‎.

کلیدواژه‌ها
‎Division ring‎, ‎almost subnormal subgroup‎, ‎locally soluble