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Multicasting was initially designed for stationary scenarios and does not consider extra requirements for mobile stations. Multicast membership protocols such as IGMP should be carefully evaluated whether they are completely suitable or should make some extensions or modification for wireless environments. The bandwidth constraints and variable conditions of radio networks require a compact, adaptive multicast group management protocol, which should minimize the packet interchanging between the mobile host and the multicast router. This paper differs from previous work in that it concerns multicasting in a single cell IEEE 802.11 network. Formulas for calculating the total and partial channel capture time by the IGMP traffic are presented, and then we provide a method for calculating the reliability of the standard IGMP management scheme. We present a new dynamic group management algorithm which provides constant reliability, automatically adapting to the channel conditions. Some improvements regarding the processing and forwarding of multicast frames are also presented.