many results were proved on the structure of finite groups with some‎ ‎restrictions on their real elements and on their conjugacy classes‎. ‎we‎ ‎generalize a few of these to some classes of infinite groups‎. ‎we study groups in which real elements are central‎, ‎groups in which real elements are $2$-elements‎, ‎groups in which all non-trivial classes have the same finite size and $fc$-groups w...

Let F be a field of characteristic 6= 2. Let G be an algebraic group defined over F . An element t ∈ G(F ) is called real if there exists s ∈ G(F ) such that sts = t. A semisimple element t in GLn(F ), SLn(F ), O(q), SO(q), Sp(2n) and the groups of type G2 over F is real if and only if t = τ1τ2 where τ 2 1 = ±1 = τ 2 2 (ref. [ST1, ST2]). In this paper we extend this result to the semisimple ele...

Hysteresis is a phenomenon that has been observed across many different materials and situations. Under small-amplitude cyclical motion, classical hysteresis designates a constant loss per cycle over a wide range of frequencies. This is also consistent with an increase in losses or attenuation with frequency that is strictly proportional to the first power of frequency. Unfortunately, the class...