Groups generated by two bicyclic units in integral group rings
نویسندگان
چکیده
منابع مشابه
Involutions and Free Pairs of Bicyclic Units in Integral Group Rings of Non-nilpotent Groups
If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...
متن کاملInvolutions and Free Pairs of Bicyclic Units in Integral Group Rings
If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...
متن کاملBass Units as Free Factors in Integral Group Rings of Simple Groups
Let G be a finite group, u a Bass unit based on an element a of G of prime order, and assume that u has infinite order modulo the center of the units of the integral group ring ZG. It was recently proved that if G is solvable then there is a Bass unit or a bicyclic unit v and a positive integer n such that the group generated by un and vn is a non-abelian free group. It has been conjectured tha...
متن کاملInvolutions and Free Pairs of Bass Cyclic Units in Integral Group Rings
Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let ∗ be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (uk,m(x), uk,m(x ∗)), or (uk,m(x), uk,m(y)), formed respectively by Bass cyclic and ∗-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG. 1....
متن کاملTorsion Units in Integral Group Rings of Conway Simple Groups
Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005