TY - JOUR
ID - 54649
TI - A Characterization of the Small Suzuki Groups by the Number of the Same Element Order
JO - Journal of Sciences, Islamic Republic of Iran
JA - JSCIENCES
LA - en
SN - 1016-1104
AU - Parvizi Mosaed, H.
AU - Iranmanesh, A.
AU - Tehranian, A.
AD - 1Department of Mathematics, Faculty of Basic Sciences, Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran
AD - 2Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran
Y1 - 2015
PY - 2015
VL - 26
IS - 2
SP - 171
EP - 177
KW - Element order
KW - Sylow subgroup
KW - Simple -group
KW - Suzuki group
DO -
N2 - Suppose that is a finite group. Then the set of all prime divisors of is denoted by and the set of element orders of is denoted by . Suppose that . Then the number of elements of order in is denoted by and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if is a group such that , where , then . Here denotes the family of Suzuki simple groups, , . This proves that the second and third member of the family of Suzuki simple groups are characterizable by the set of the number of the same element order.
UR - https://jsciences.ut.ac.ir/article_54649.html
L1 - https://jsciences.ut.ac.ir/article_54649_b9016d7ddd6b44de3979a6084b8ac13e.pdf
ER -