Arithmetic progressions in finite groups
Keyword(s):
In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio [Formula: see text]. This extends the case [Formula: see text] studied in previous papers [R. Brandl and W. Shi, Finite groups whose element orders are consecutive integers, J. Algebra 143 (1991) 388–400; Y. Feng, Finite groups whose abelian subgroup orders are consecutive integers, J. Math. Res. Exp. 18 (1998) 503–506; W. Shi, Finite groups whose proper subgroup orders are consecutive integers, J. Math. Res. Exp. 14 (1994) 165–166].
1991 ◽
Vol 143
(2)
◽
pp. 388-400
◽
1968 ◽
Vol 11
(3)
◽
pp. 409-414
◽
2009 ◽
Vol 05
(04)
◽
pp. 625-634
2008 ◽
Vol 78
(3)
◽
pp. 431-436
◽
Keyword(s):