Affiliation:
1. Liceo G. B. Benedetti – N. Tommaseo , Castello 2835 – 30122 , Venezia , Italy
Abstract
Abstract
In this paper, we prove that if 𝐺 is a group generated by elements of order two with the property that the product of any two such elements has order 1, 2, 3 or 5 with all possibilities occurring, then
G
≃
A
5
G\simeq A_{5}
or
G
≃
PSU
(
3
,
4
)
G\simeq\mathrm{PSU}(3,4)
.
This provides an affirmative answer to Problem 19.36 in the Kourovka notebook.
Subject
Algebra and Number Theory
Reference17 articles.
1. M. Aschbacher,
On finite groups generated by odd transpositions. I,
Math. Z. 127 (1972), 45–56.
2. M. Aschbacher,
On finite groups generated by odd transpositions. II,
J. Algebra 26 (1973), 451–459.
3. M. Aschbacher,
On finite groups generated by odd transpositions. III,
J. Algebra 26 (1973), 460–478.
4. M. Aschbacher,
On finite groups generated by odd transpositions. IV,
J. Algebra 26 (1973), 479–491.
5. M. Aschbacher,
3-Transposition Groups,
Cambridge Tracts in Math. 124,
Cambridge University, Cambridge, 1997.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献