Equation 677 Database

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Magma c45312e0ee53…

magma c45312e0ee53
Size
595
Isomorphism class hash
c45312e0ee536594dbb03dd8f0c420a0d0ce9deead6a94567187fc4d089046fa
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 00:47:38
Display reorder
351,353,352,349,350,348,336,341,337,338,339,340,500,498,501,502,503,499,346,345,347,342,343,344,504,505,506,507,508,509,555,556,593,557,594,410,409,411,412,413,408,397,396,398,399,400,401,391,390,392,393,394,395,384,389,385,386,387,388,274,273,275,271,270,272,280,276,279,277,278,281,402,407,403,404,405,406,253,252,254,257,255,256,79,78,77,81,82,80,98,100,99,97,95,96,176,178,177,175,174,173,223,222,224,227,225,226,5,4,3,2,1,0,85,84,83,88,86,87,90,89,91,94,92,93,180,181,179,184,182,183,534,552,547,542,511,523,517,527,538,585,565,560,575,580,588,570,420,425,421,422,423,424,479,484,480,481,482,483,426,431,427,428,429,430,435,434,436,437,432,433,485,490,486,487,488,489,492,494,491,495,496,493,418,417,419,414,415,416,269,268,267,264,265,266,169,168,167,171,172,170,112,111,110,108,109,107,209,208,207,204,206,205,235,234,236,239,237,238,163,162,161,166,164,165,200,198,199,203,201,202,101,103,102,105,106,104,155,157,156,160,158,159,533,553,549,544,514,524,519,529,539,587,567,562,577,582,591,572,497,454,450,451,452,453,464,463,465,466,461,462,478,477,473,474,475,476,471,470,472,467,468,469,442,441,443,438,439,440,449,445,448,446,447,444,458,457,459,460,455,456,259,258,260,263,261,262,116,118,117,115,113,114,146,148,147,145,143,144,127,126,125,129,130,128,233,232,231,228,229,230,120,119,121,123,124,122,135,134,136,132,133,131,153,152,154,151,149,150,141,140,142,137,138,139,532,550,546,541,510,522,515,526,537,583,563,558,573,579,592,569,311,310,306,307,308,309,318,323,319,320,321,322,332,331,333,334,335,330,325,324,326,327,328,329,298,297,299,294,295,296,305,301,304,302,303,300,312,317,313,314,315,316,244,243,245,242,241,240,15,17,16,14,12,13,41,43,42,46,44,45,25,24,23,27,28,26,215,214,213,211,210,212,19,18,20,185,22,21,33,32,34,30,31,29,48,47,49,52,50,51,39,38,40,35,36,37,530,551,545,540,512,520,516,525,535,584,564,559,574,578,589,568,364,363,365,360,361,362,376,375,377,372,373,374,370,369,371,366,367,368,383,382,378,379,380,381,293,292,288,289,290,291,283,285,282,286,287,284,356,355,357,358,359,354,250,249,251,248,246,247,194,192,193,196,197,195,63,62,64,59,60,61,66,65,67,68,69,70,220,219,221,218,216,217,7,6,8,10,11,9,190,189,191,186,188,187,55,54,53,56,57,58,75,74,76,71,72,73,531,554,548,543,513,521,518,528,536,586,566,561,576,581,590,571 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = the submagma generated by {0, 12} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-09 00:47:39 · history