Equation 677 Database

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Magma e02203cc7ee3…

magma e02203cc7ee3
Size
396
Isomorphism class hash
e02203cc7ee32ac7cf400328f3d3aa3d54064f39a96406780fe062b44db80ae6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 05:44:08
Display reorder
395,367,312,350,306,185,309,63,1,186,13,64,2,187,14,65,3,188,15,66,4,189,16,317,307,338,310,318,5,190,17,67,6,191,18,68,7,192,19,69,8,193,20,70,9,183,21,71,10,336,311,319,308,337,22,72,11,23,184,73,12,61,53,54,55,56,57,58,59,60,315,62,316,313,314,355,385,390,384,387,333,125,247,240,170,126,248,241,171,127,249,242,161,128,250,243,162,129,251,244,163,130,252,363,358,326,253,234,164,131,254,235,165,124,343,341,352,366,344,342,332,132,255,236,166,133,256,237,167,327,364,362,168,134,245,238,135,169,246,239,119,111,112,113,114,115,116,117,118,120,121,122,123,110,325,381,375,393,388,373,354,360,201,281,40,209,202,282,41,210,203,283,42,211,204,280,43,212,205,287,44,213,206,288,45,214,207,290,46,215,208,292,47,216,194,294,48,217,195,296,49,218,196,298,50,219,197,300,51,220,198,302,52,221,199,39,304,222,200,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,394,379,376,378,359,339,347,30,180,223,266,31,181,224,267,32,182,225,257,33,334,340,365,34,172,226,258,35,173,227,259,36,174,228,260,37,175,229,261,38,353,368,345,24,176,230,262,25,177,231,263,26,178,232,264,27,179,233,265,28,361,335,346,29,108,100,101,102,103,104,105,106,107,109,98,99,323,324,357,383,377,391,386,372,320,351,152,268,85,147,153,269,86,136,154,270,74,137,155,271,75,138,156,272,76,139,157,273,77,140,158,274,78,141,159,275,79,328,330,348,356,329,331,349,80,142,160,276,81,143,148,277,82,144,149,278,83,145,150,84,279,146,151,0,87,88,89,90,91,92,93,94,95,96,97,321,322,371,380,389,382,392 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#5e76c6d3b965544f3246a1396d58a622a92ac5abe1044f6db52aefba39d6a87c, M = {75} 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, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-02 05:44:09 · history