The standard correspondence between the normal subgroups of the group G and some ideals of the group algebra FG is described. There is the problem of what we can say (or even prove) about a two-sided ideal \documentclass[12pt]{minimal}
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$$I \neq (0)$$
\end{document} of \documentclass[12pt]{minimal}
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$${\mathbb{F}}G$$
\end{document} that does not contain any element of the form 1 − g ≠ 0, g ∈G of the standard basis of the augmentation ideal of \documentclass[12pt]{minimal}
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$${\mathbb{F}}G$$
\end{document} . The main part of the argument of [2] yields the insight that, for such an ideal I there exists an expansion \documentclass[12pt]{minimal}
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$$H \supseteq G$$
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$${\mathbb{F}}H$$
\end{document} spanned by I contains an element 1 − h, h ∈ H \ G. Using the ideas of [2], we construct \documentclass[12pt]{minimal}
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$${\mathbb{F}}$$
\end{document} -thick groups H such that for every ideal J ≠ (0) of \documentclass[12pt]{minimal}
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$${\mathbb{F}}H$$
\end{document} there are elements 1 − h ≠ 0 in J. This construction allows many variations. Examples of simple \documentclass[12pt]{minimal}
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$${\mathbb{F}}$$
\end{document} -thick groups were pointed out in [2]. A natural class of (in general non-simple) \documentclass[12pt]{minimal}
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$${\mathbb{F}}$$
\end{document} -full groups are the normal sections of the groups
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$$S^{\prime} := \rm{Sym}({\it M})/ \rm{Fin}({\it M})\,\rm{for\,any\,infinite\,set} {\it M}.$$
\end{document}(Here, Fin(M) is the subgroup of all finitary permutations of M.)
