Equation 677 Database

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Magma 0cad214bd0a2…

magma 0cad214bd0a2
Size
705
Isomorphism class hash
0cad214bd0a2e8edda843ce927d952e7a74ff9aa16587799981c2e2370cea347
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 17:45:03
Display reorder
660,107,523,59,440,253,105,524,57,441,251,106,522,58,439,252,519,103,55,436,256,520,104,56,437,254,521,102,54,438,255,98,514,50,431,259,96,515,48,432,257,97,513,49,430,258,517,101,53,434,262,518,99,51,435,260,516,100,52,433,261,663,670,666,662,126,428,392,606,163,127,429,393,607,161,128,427,391,605,162,424,129,388,602,166,425,130,389,603,164,426,131,390,604,165,124,419,383,597,158,125,420,384,598,159,123,418,382,596,160,422,120,386,600,157,423,121,387,601,155,421,122,385,599,156,689,685,687,686,302,196,138,464,535,303,194,139,465,536,304,195,140,463,534,192,301,141,460,531,193,299,142,461,532,191,300,143,462,533,308,202,136,455,526,309,200,137,456,527,310,201,135,454,525,198,307,132,458,529,199,305,133,459,530,197,306,134,457,528,664,667,672,668,9,511,337,356,174,10,512,338,357,175,11,510,339,355,173,507,8,336,352,177,508,6,334,353,178,509,7,335,354,176,1,502,343,347,172,0,503,344,348,170,2,501,345,346,171,505,3,342,350,168,506,4,340,351,169,504,5,341,349,167,674,680,679,682,182,570,266,618,404,183,571,267,619,405,184,569,268,617,403,566,181,265,614,400,567,179,263,615,401,568,180,264,616,402,188,561,272,609,395,189,562,273,610,396,190,560,274,608,394,564,187,271,612,398,565,185,269,613,399,563,186,270,611,397,671,661,669,665,249,558,233,582,21,250,559,234,583,22,248,557,235,581,23,554,245,236,578,20,555,246,237,579,18,556,247,238,580,19,240,549,231,573,12,241,550,232,574,13,239,548,230,572,14,552,243,227,576,15,553,244,228,577,16,551,242,229,575,17,697,693,696,698,318,144,547,476,323,319,658,659,656,657,317,151,546,475,324,153,321,543,472,326,154,322,544,473,327,152,320,545,474,325,316,150,538,467,329,314,148,539,468,330,315,149,537,466,328,146,312,541,470,332,147,313,542,471,333,145,311,540,469,331,701,702,703,704,31,283,41,653,652,32,281,39,655,654,30,282,40,650,651,286,34,37,644,645,284,35,38,647,646,285,33,36,649,648,29,278,47,635,634,27,279,45,637,636,28,280,46,633,632,277,25,43,640,641,275,26,44,643,642,276,24,42,638,639,700,699,694,695,219,487,68,90,114,220,488,66,91,115,218,486,67,92,116,483,215,71,93,117,484,216,69,94,118,485,217,70,95,119,225,478,63,88,112,226,479,64,89,113,224,477,65,87,111,481,221,62,84,108,482,222,60,85,109,480,223,61,86,110,673,683,678,684,298,416,452,594,380,296,417,453,595,381,297,415,451,593,379,412,294,448,590,376,413,295,449,591,377,414,293,450,592,378,289,407,443,585,371,287,408,444,586,372,288,406,442,584,370,410,292,446,588,374,411,290,447,589,375,409,291,445,587,373,681,675,676,677,206,361,81,499,630,207,362,82,500,631,208,363,83,498,629,360,205,80,495,626,358,203,78,496,627,359,204,79,497,628,212,367,72,490,621,213,368,73,491,622,214,369,74,489,620,366,211,75,493,624,364,209,76,494,625,365,210,77,492,623,688,690,691,692 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#61e4460e7132ae46985bdc51b44ba41f1d8967bba1a2e054d2c046422600ec54, 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 17:45:05 · history