Group type class with helper class and implicit class for syntax

GroupAnyVal.scala

object GroupSyntax {
  implicit class GroupOps[T](val x: T) extends AnyVal {
    def |+|(y: T)(implicit ev: Group[T]): T = ev.plus(x, y)
    def inverse(implicit ev: Group[T]): T = ev.inverse(x)
    def |-|(y: T)(implicit ev: Group[T]): T = ev.minus(x, y)
  }

  def zero[T: Group]: T = Group[T].zero
}

GroupAnyVal2.scala

object GroupSyntax {
  class GroupOps[T](val x: T) extends AnyVal { ... }
  implicit def toGroupOps[T](x: T) = new GroupOps(x)
  //...
}

GroupSyntax.scala

object GroupSyntax {
  implicit class GroupOps[T: Group](x: T) {
    def |+|(y: T): T = Group[T].plus(x, y)
    def inverse: T = Group[T].inverse(x)
    def |-|(y: T): T = Group[T].minus(x, y)
  }

  def zero[T: Group]: T = Group[T].zero
}

GroupSyntax2.scala

object GroupSyntax {
  class GroupOps[T: Group](x: T) { ... }
  implicit def toGroupOps[T: Group](x: T) = new GroupOps(x)
  //...
}

Test.scala

import GroupSyntax._

implicit def PairGroup[T1: Group, T2: Group]: Group[(T1, T2)] =
  new GroupAux[(T1, T2)](
    (zero[T1], zero[T2]),
    (x, y) => (x._1 |+| y._1, x._2 |+| y._2),
    x => (x._1.inverse, x._2.inverse)
  )

def sum[T: Group](elems: Seq[T]): T = elems.foldLeft(zero[T]) { _ |+| _ }

def sumDifference[T: Group](elems1: Seq[T], elems2: Seq[T]): T =
  sum(elems1) |-| sum(elems2)