Equation 677 Database

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Magma 573d80bab7af…

magma 573d80bab7af
Size
705
Isomorphism class hash
573d80bab7aff09e5020b185ade10fbc22181a17a62b81e033dc401cdedcc355
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 16:51:10
Display reorder
660,434,295,422,98,254,96,296,432,420,252,294,97,433,421,253,298,437,425,101,257,435,299,423,99,255,297,436,424,100,256,429,293,417,104,260,430,291,418,102,258,431,292,419,103,259,289,428,416,107,263,290,426,414,105,261,288,427,415,106,262,663,661,665,666,338,57,360,350,326,348,58,336,361,324,59,349,337,362,325,56,341,363,353,329,339,54,364,351,327,55,340,365,352,328,344,63,366,356,332,342,64,367,354,330,343,65,368,355,331,62,347,369,359,335,60,345,370,357,333,61,346,371,358,334,688,690,686,689,476,183,614,566,133,564,184,474,612,134,185,565,475,613,132,182,479,617,569,136,477,180,615,567,137,181,478,616,568,135,471,189,609,561,139,472,190,610,562,140,473,191,611,563,138,188,470,608,560,142,186,468,606,558,143,187,469,607,559,141,664,672,662,669,530,66,446,506,379,504,67,528,444,380,68,505,529,445,378,69,533,449,509,382,531,70,447,507,383,71,532,448,508,381,525,72,441,501,377,526,73,442,502,375,527,74,443,503,376,75,524,440,500,373,76,522,438,498,374,77,523,439,499,372,680,675,682,678,590,385,542,554,602,552,386,588,540,600,384,553,589,541,601,388,593,545,557,605,591,389,543,555,603,387,592,544,556,604,585,391,537,549,597,586,392,538,550,598,587,390,539,551,599,394,584,536,548,596,395,582,534,546,594,393,583,535,547,595,670,667,671,668,285,175,123,115,270,116,176,286,124,271,174,114,287,125,272,178,284,122,118,273,282,179,120,119,274,177,283,121,117,275,276,173,129,113,268,277,171,130,111,269,278,172,131,112,267,169,279,128,109,264,170,280,126,110,265,168,281,127,108,266,696,697,694,693,644,44,646,645,647,639,42,638,636,637,43,641,640,642,643,47,657,658,656,659,649,45,650,648,651,46,653,654,652,655,81,50,619,495,38,82,48,620,496,36,83,49,618,497,37,53,80,622,494,41,51,78,623,492,39,52,79,621,493,40,701,703,704,702,629,148,160,307,628,308,149,624,161,625,147,306,627,159,626,144,635,156,310,634,631,145,157,311,630,146,633,158,309,632,399,154,166,305,467,400,155,167,303,465,401,153,165,304,466,150,398,162,301,463,151,396,163,302,464,152,397,164,300,462,699,695,700,698,95,250,518,578,458,576,251,93,516,456,249,577,94,517,457,246,91,521,581,461,92,247,519,579,459,248,90,520,580,460,86,241,513,573,453,84,242,514,574,454,85,240,515,575,455,244,89,512,572,452,245,87,510,570,450,243,88,511,571,451,673,679,676,683,322,3,27,488,410,486,4,323,28,408,5,487,321,29,409,2,318,26,491,413,319,1,24,489,411,0,320,25,490,412,313,9,33,483,405,314,10,34,484,406,312,11,35,485,407,8,316,32,482,404,6,317,30,480,402,7,315,31,481,403,684,681,674,677,192,17,216,213,238,214,15,193,217,239,16,215,194,218,237,13,195,219,212,234,196,14,220,210,235,12,197,221,211,236,198,23,222,204,229,199,21,223,205,230,200,22,224,206,228,19,201,225,207,232,20,202,226,208,233,18,203,227,209,231,685,691,687,692 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#40ac4fa024666665509cd5e942b6a945fc35db692a456c0e176de1fe3e839a09, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:51:11 · history