Equation 677 Database

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Magma a71bbc278a0c…

magma a71bbc278a0c
Size
705
Isomorphism class hash
a71bbc278a0cfa0f357231183eea96b5ccc8cee182eb51f26d3cb4cccfe6ca1f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 16:49:39
Display reorder
660,543,51,556,558,552,576,563,572,52,578,583,592,53,596,598,603,50,612,616,618,623,48,632,636,638,643,49,652,656,658,57,500,512,516,518,520,58,532,536,538,59,480,492,496,498,56,421,424,426,428,54,443,450,454,456,55,460,470,474,476,699,692,688,686,548,102,559,557,547,579,568,567,103,577,588,587,104,599,597,608,105,607,619,617,628,106,627,639,637,648,107,647,659,657,100,508,507,519,517,528,101,527,539,537,99,488,487,499,497,96,434,433,429,427,97,447,446,457,455,98,467,466,477,475,695,702,698,691,233,74,242,255,271,240,231,272,72,256,232,270,73,241,257,229,77,274,245,254,230,75,275,243,252,228,76,273,244,253,80,239,269,248,261,237,78,267,246,262,79,238,268,247,263,83,235,265,251,260,81,236,266,249,258,82,234,264,250,259,661,681,675,669,414,157,142,153,378,143,415,379,158,154,416,380,156,141,155,417,160,381,138,152,418,161,382,139,150,419,159,383,140,151,163,412,376,133,144,413,164,377,134,145,162,411,375,132,146,166,408,372,136,147,167,409,373,137,148,165,410,374,135,149,676,670,672,680,549,115,550,546,542,570,569,562,116,566,589,582,114,590,586,609,118,602,610,606,629,119,622,630,626,649,117,642,650,646,113,509,503,510,506,529,111,523,530,526,112,489,483,490,486,109,423,420,435,432,110,448,442,449,445,108,468,463,469,465,697,704,693,700,541,319,555,553,540,575,561,560,320,573,580,581,318,595,593,601,322,600,615,613,621,323,620,635,633,640,321,641,655,653,317,502,501,515,513,522,315,521,535,533,316,482,481,495,493,313,430,431,437,436,314,440,441,453,451,312,461,462,473,471,701,694,703,696,544,131,545,554,551,565,564,571,129,574,584,591,130,585,594,604,127,611,605,614,624,128,631,625,634,644,126,651,645,654,122,504,511,505,514,524,120,531,525,534,121,484,491,485,494,125,439,438,422,425,123,459,458,444,452,124,479,478,464,472,689,690,685,687,94,34,330,342,354,331,95,355,35,343,93,356,33,332,344,90,30,357,333,345,91,31,358,334,346,92,32,359,335,347,25,85,352,328,340,86,26,353,329,341,24,84,351,327,339,28,88,348,324,336,29,89,349,325,337,27,87,350,326,338,665,664,667,673,218,178,16,43,211,17,216,212,179,44,217,210,177,15,42,221,174,214,12,46,219,175,215,13,47,220,176,213,14,45,169,224,209,22,41,222,170,207,23,39,168,223,208,21,40,172,227,205,18,37,173,225,206,19,38,171,226,204,20,36,662,684,678,671,402,69,278,293,300,276,403,301,70,291,404,302,71,277,292,405,68,303,281,289,406,66,304,279,290,407,67,305,280,288,60,400,306,284,299,401,61,307,282,297,62,399,308,283,298,63,396,309,287,295,64,397,310,285,296,65,398,311,286,294,683,679,682,677,202,0,366,390,190,367,203,191,2,391,201,189,1,368,392,198,4,186,369,393,199,5,187,370,394,200,3,188,371,395,7,193,181,364,388,194,8,182,365,389,6,192,180,363,387,10,196,184,360,384,11,197,185,361,385,9,195,183,362,386,674,668,666,663 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#3f658a46fc44ddfd8c713ec5e3bbc16ee9055426ab1786d448b9cc156d806e6f, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 16:49:41 · history