Equation 677 Database

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Magma cb73dce10441…

magma cb73dce10441
Size
451
Isomorphism class hash
cb73dce10441cb4efd7515efc925d27362f361ff58a6a9e6ee813fd8878e6c63
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 22:27:22
Display reorder
447,449,450,446,442,444,441,443,445,448,440,106,301,21,44,204,78,329,265,141,173,107,302,22,45,205,79,330,266,142,174,303,108,23,46,206,72,331,267,143,175,296,109,16,47,207,73,332,268,136,168,297,110,17,40,200,74,333,269,137,169,41,111,298,18,201,75,334,270,138,170,299,104,19,202,76,139,335,271,171,42,300,105,20,43,203,77,328,264,140,172,232,255,233,235,236,237,238,234,401,399,437,358,404,406,403,385,387,410,411,409,438,368,414,416,413,395,397,420,419,421,432,378,424,425,423,405,407,427,429,430,433,388,354,356,353,415,417,360,359,361,434,398,364,366,363,428,431,370,408,371,369,439,374,376,373,355,357,380,379,381,435,384,386,367,383,365,390,418,389,391,436,426,394,396,393,375,377,400,392,402,412,352,362,372,382,422,115,310,5,51,213,85,338,274,150,182,116,311,6,52,214,86,339,275,151,183,304,117,7,53,215,87,340,276,144,176,305,118,1,54,208,80,341,277,145,177,306,119,0,55,209,81,342,278,146,178,48,112,307,2,210,82,343,279,147,179,308,113,3,211,83,148,336,272,180,49,309,114,4,50,212,84,337,273,149,181,246,239,240,242,243,244,245,241,101,292,12,36,199,67,321,258,129,161,102,293,13,37,193,68,320,259,128,160,294,103,14,38,192,69,322,260,130,162,295,97,15,39,194,70,323,261,131,163,289,96,8,33,195,71,324,262,132,164,32,98,288,9,196,65,325,263,133,165,290,99,10,197,64,134,326,257,166,34,291,100,11,35,198,66,327,256,135,167,225,224,226,228,229,230,231,227,123,318,30,59,221,93,346,282,158,190,124,319,31,60,222,94,347,283,159,191,312,125,24,61,223,95,348,284,152,184,313,126,25,62,216,88,349,285,153,185,314,127,26,63,217,89,350,286,154,186,56,120,315,27,218,90,351,287,155,187,316,121,28,219,91,156,344,280,188,57,317,122,29,58,220,92,345,281,157,189,254,247,248,250,251,252,253,249 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#d07de435ce6a0cf7445c6bc758855835696b56d3c480b19b02766bd6e1b305ed, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + 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: 11.

last edited by qawbecrdtey at 2026-10-06 22:27:23 · history