${\mathrm{Al}}_{52.5}$${\mathrm{Ge}}_{22.5}$${\mathrm{Mn}}_{25}$, ${\mathrm{Al}}_{52.5}$${\mathrm{Ge}}_{22.5}$${\mathrm{Mn}}_{24.85}$${\mathrm{Fe}}_{0.15}$, ${\mathrm{Al}}_{40}$${\mathrm{Cu}}_{10}$${\mathrm{Ge}}_{25}$${\mathrm{Mn}}_{25}$, and ${\mathrm{Al}}_{40}$${\mathrm{Cu}}_{9.94}$${\mathrm{Fe}}_{0.06}$${\mathrm{Ge}}_{25}$${\mathrm{Mn}}_{25}$ icosahedral alloys and AlGeMn and ${\mathrm{AlGeMn}}_{0.995}$${\mathrm{Fe}}_{0.005}$ crystalline alloys have been studied with x-ray diffraction, differential thermal analysis, magnetization, and $^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy. It is found that AlGeMn, a ferromagnet, is the major second phase present in the samples of icosahedral Al-Ge-Mn and Al-Cu-Ge-Mn systems, and is thus partially responsible for the observed ferromagnetism in these alloys. This ferromagnet is also the main crystallization product of these systems. Room-temperature $^{57}\mathrm{Fe}$ M\"ossbauer spectra show that Fe atoms in these systems bear no magnetic moment and are distributed among a multiplicity of sites, which is interpreted as evidence of intrinsic disorder present in icosahedral alloys. Analysis of 4.2-K M\"ossbauer spectra shows that less than half of the Fe atoms possess a very small magnetic moment in both systems, which is the first direct evidence supporting the notion of two classes of transition-metal sites in Al-based icosahedral alloys. It is argued that the magnetic moment of Mn atoms in these systems as well as the Curie temperatures must be very small. It is noted that annealing of rapidly quenched Al-Ge-Mn and Al-Cu-Ge-Mn alloys leads to the occurrence of high values of coercive force and saturation magnetization.
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