Equation 677 Database

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Magma 4ccca7b362fe…

magma 4ccca7b362fe
Size
705
Isomorphism class hash
4ccca7b362fe2e903fedb5a37bce7e566b74bea9f34c6b7434610c140fa19ebf
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 18:12:26
Display reorder
660,419,15,312,443,295,420,296,16,310,444,17,297,421,311,445,418,14,294,315,442,416,12,292,313,440,417,13,293,314,441,21,286,318,425,449,287,22,316,426,450,427,288,23,317,451,20,289,321,424,448,18,290,319,422,446,19,291,320,423,447,672,663,664,661,73,1,358,43,407,74,408,0,359,44,2,409,72,360,42,76,3,406,361,46,77,4,404,362,47,75,5,405,363,45,6,413,364,79,41,414,7,365,80,39,78,415,8,366,40,9,412,367,82,37,10,410,368,83,38,11,411,369,81,36,687,690,688,686,455,172,195,238,255,456,253,173,193,239,174,254,457,194,240,454,175,251,191,241,452,176,252,192,242,453,177,250,190,243,170,261,201,461,244,259,171,199,462,245,463,260,169,200,246,166,257,197,460,247,167,258,198,458,248,168,256,196,459,249,667,665,666,669,385,94,381,491,585,386,586,95,379,492,93,587,387,380,493,384,90,584,377,490,382,91,582,378,488,383,92,583,376,489,85,591,372,391,497,592,86,370,392,498,393,593,84,371,499,88,590,375,390,496,89,588,373,388,494,87,589,374,389,495,681,675,678,674,98,322,503,631,561,96,562,323,504,632,324,563,97,505,633,101,325,560,502,630,99,326,558,500,628,100,327,559,501,629,328,567,509,104,637,568,329,510,102,638,103,569,330,511,639,331,566,508,107,636,332,564,506,105,634,333,565,507,106,635,670,662,671,668,515,179,573,431,228,516,226,180,574,432,178,227,517,575,433,514,182,231,572,430,512,183,229,570,428,513,181,230,571,429,185,234,579,521,437,232,186,580,522,438,523,233,184,581,439,188,237,578,520,436,189,235,576,518,434,187,236,577,519,435,693,695,694,697,163,152,621,397,548,164,549,150,622,398,151,550,165,623,399,162,155,551,620,396,160,153,552,618,394,161,154,553,619,395,147,554,627,156,403,655,148,654,653,652,657,658,149,659,656,146,555,626,157,402,144,556,624,158,400,145,557,625,159,401,703,701,702,704,527,112,609,123,341,528,342,113,610,124,111,340,529,611,125,526,108,344,608,122,524,109,345,606,120,525,110,343,607,121,118,339,615,533,129,337,119,616,534,130,535,338,117,617,131,114,335,614,532,128,115,336,612,530,126,116,334,613,531,127,700,696,698,699,280,225,25,597,467,281,468,223,26,598,224,469,282,24,599,283,221,466,28,596,284,222,464,29,594,285,220,465,27,595,216,473,31,278,603,474,214,32,279,604,277,475,215,30,605,219,472,34,274,602,217,470,35,275,600,218,471,33,276,601,676,680,682,684,643,137,479,356,69,644,70,135,480,357,136,71,645,481,355,642,133,68,478,352,640,134,66,476,353,641,132,67,477,354,143,60,485,649,347,61,141,486,650,348,651,62,142,487,346,139,63,484,648,350,140,64,482,646,351,138,65,483,647,349,673,683,679,677,51,206,267,300,539,52,540,207,265,298,205,541,53,266,299,50,202,538,263,303,48,203,536,264,301,49,204,537,262,302,212,545,273,57,306,546,213,271,58,304,59,547,211,272,305,208,544,269,56,309,209,542,270,54,307,210,543,268,55,308,689,691,692,685 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#69e303b0df9a949f679bcb1932ca3e0d44707fb71c41006ed01ea0a3f8179ab7, 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 18:12:27 · history