A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties order-embedding the power set lattice of the positive integers. Based on this result, several examples of finite involution monoids with extreme varietal properties are exhibited. These examples—all first of their kinds—include the following: finite involution monoids that generate huge varieties but whose reduct monoids generate Cross varieties; two finite involution monoids sharing a common reduct monoid such that one generates a huge, non-finitely based variety while the other generates a Cross variety; and two finite involution monoids that generate Cross varieties, the join of which is huge.

中文翻译：

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具有极端特性的各种对合半定式

包含多个子变体的连续体的变体据说是巨大的。建立了一个充分条件，在该条件下，对合mono极体因其子变量晶格有序嵌入正整数的幂集晶格而产生了巨大的变化。基于此结果，展示了具有极度多样性特性的有限对合半边形的几个示例。这些例子（包括所有种类的例子）包括：产生有限个对合体的类，它们产生巨大的变体，而其归约类的半体则产生Cross变体；共享一个共同的归约monoid的两个有限对合Monoid，从而一个产生巨大的，非有限的变种，而另一个产生Cross变种；和两个产生Cross变体的有限对合Monoid，它们的连接很大。