diff --git a/src/DirectProducts.jl b/src/DirectProducts.jl
index d6d5a11..c833daa 100644
--- a/src/DirectProducts.jl
+++ b/src/DirectProducts.jl
@@ -102,8 +102,8 @@ end
 #
 ###############################################################################
 
-elem_type(G::DirectProductGroup{T}) where {T} =
-   DirectProductGroupElem{elem_type(G.group)}
+elem_type(::Type{DirectProductGroup{T}}) where {T} =
+   DirectProductGroupElem{elem_type(T)}
 
 parent_type(::Type{DirectProductGroupElem{T}}) where {T} =
    DirectProductGroup{parent_type(T)}
diff --git a/src/FreeGroup.jl b/src/FreeGroup.jl
index ef8f911..c502cf3 100644
--- a/src/FreeGroup.jl
+++ b/src/FreeGroup.jl
@@ -13,8 +13,7 @@ FreeGroupElem = GroupWord{FreeSymbol}
 
 mutable struct FreeGroup <: AbstractFPGroup
    gens::Vector{FreeSymbol}
-   #     order::Vector{T}
-   #     fastmult_table::Array{Int,2}
+
    function FreeGroup{T<:GSymbol}(gens::Vector{T})
       G = new(gens)
       G.gens = gens
@@ -30,9 +29,9 @@ export FreeGroupElem, FreeGroup
 #
 ###############################################################################
 
-parent_type(::Type{FreeGroupElem}) = FreeGroup
+elem_type(::Type{FreeGroup}) = FreeGroupElem
 
-elem_type(::FreeGroup) = FreeGroupElem
+parent_type(::Type{FreeGroupElem}) = FreeGroup
 
 ###############################################################################
 #
diff --git a/src/WreathProducts.jl b/src/WreathProducts.jl
index 5232446..08ed9ad 100644
--- a/src/WreathProducts.jl
+++ b/src/WreathProducts.jl
@@ -49,7 +49,7 @@ end
 #
 ###############################################################################
 
-elem_type(::WreathProduct{T, I}) where {T, I} = WreathProductElem{elem_type(T), I}
+elem_type(::Type{WreathProduct{T, I}}) where {T, I} = WreathProductElem{elem_type(T), I}
 
 parent_type(::Type{WreathProductElem{T, I}}) where {T, I} =
    WreathProduct{parent_type(T), I}