On generalized quotient MI-groups

Many identities group (MI-group, for short) is an algebraic structure generalizing the group structure, where an involutive anti-automorphism satisfying certain properties is used instead of the standard group inversion. The concept of MI-group, in a more general form than in this article, has been introduced by Holčapek and Å těpnička in the paper “MI-algebras: A new frame work for arithmetics of (extensional) fuzzy numbers” to describe properties of different approaches to arithmetics of vaguely specified quantities (e.g., stochastic or fuzzy quantities) in a unified way. This article is a continuation of the effort to develop the theory of MI-groups and is focused on a generalization of the construction of quotient MI-groups induced by so-called normal full MI-subgroups which has been introduced by Holčapek et al. recently in the paper “Quotient MI-groups”. Besides a more general definition of quotient MI-groups, we prove three isomorphism theorems for MI-groups in this new framework.