Equation 677 Database

← all  ·  ← by size  ·  ← size 341

Magma dad9d3b089a7…

magma dad9d3b089a7
Size
341
Isomorphism class hash
dad9d3b089a76812d74ae61e24b927c00ec3dd43be045a5526c1ebadbaa75fd8
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 340) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:04:52
Display reorder
340,175,176,172,173,171,178,174,195,200,198,199,203,201,197,194,192,177,179,193,233,231,232,229,230,228,239,237,238,235,236,150,147,148,149,146,144,145,153,154,155,202,196,234,152,151,169,168,170,49,50,48,52,53,51,55,56,57,58,59,54,330,325,317,318,319,316,324,329,180,181,186,187,188,183,182,217,226,227,225,222,223,216,220,221,185,184,219,166,167,165,162,163,164,156,157,158,159,160,209,215,213,214,211,212,210,205,206,204,224,218,161,208,207,190,189,191,9,10,11,8,6,7,2,1,4,5,3,0,308,323,328,339,337,335,322,311,95,93,85,86,84,91,94,116,109,110,108,112,113,115,119,117,90,92,118,264,265,266,267,268,269,270,271,272,273,274,282,279,280,281,278,276,277,285,286,287,111,114,275,284,283,89,88,87,79,80,78,82,83,81,76,77,74,72,73,75,310,315,334,338,336,333,314,309,250,251,240,241,242,246,249,42,38,36,37,41,39,44,45,46,248,247,47,142,143,141,138,139,140,132,133,134,135,136,27,33,34,35,32,30,31,26,24,25,40,43,137,29,28,244,243,245,292,293,291,288,289,290,298,299,296,294,295,297,331,326,312,320,321,313,327,332,69,70,62,60,61,68,71,124,126,127,128,129,130,123,120,121,67,66,122,106,107,105,102,103,104,96,97,98,99,100,17,23,21,22,19,20,18,13,14,12,131,125,101,16,15,63,65,64,258,259,260,261,262,263,255,256,253,254,252,257,307,306,300,301,302,303,304,305 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 341 = 1 + 5*68, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#ae850597310ca1e4e432d9166a7108f5487ce49948bce500209d7acd9fde2b9f, M = {68} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 68): MacNeish's product over GF(4) x GF(17); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 1.

last edited by qawbecrdtey at 2026-10-01 23:04:53 · history