|
Gyrotransversals
of order p3
Ramjash Gurjar (1), Ratan Lal (2)
and Vipul Kakkar
(3)
(1) Department
of Mathematics,
Central
University of
Rajasthan, NH-8,
Ajmer,
India
Email address:
ramjashgurjar83@gmail.com
(2) Department of
Mathematics,
Galgotias
University, Greater
Noida, India
Email address:
vermarattan789@gmail.com
(3) Department of
Mathematics, Central
University of
Rajasthan, NH-8,
Ajmer,
India
Email address:
vplkakkar@gmail.com
Doi :
https://doi.org/10.47013/17.1.5
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
85 - 97
PDF
Received on:
March 9,
2023;
Accepted
on: Aug. 6,
2023
Abstract. In this
paper, we
compute the
isomorphism
classes of
gyrotransversals
of order p3
corresponding to
a fixed subgroup
of order p in
the group Zp⋉Zp3
, where p is an
odd prime. This
yields a lower
bound for the
number of right
gyrogroups of
order p3 upto
isomorphism. In
addition, we
obtain a lower
bound for the
non-isomorphic
right gyrogroups
of order p3 of
nilpotency class
2.
Keywords: Gyrotransversal,
Right gyrogroup,
Cauchy-Frobenius
Formula, Right
loop.
|
