Equation 677 Database

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Magma 5b53129eac6d…

magma 5b53129eac6d
Size
705
Isomorphism class hash
5b53129eac6d3fba9dc59748dcde57c8faa3ac272c7ef0ef41f818f99385b9f7
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 16:50:02
Display reorder
660,308,69,428,404,344,429,309,345,70,405,310,346,68,430,406,311,72,347,431,407,312,73,348,432,408,313,71,349,433,409,67,306,342,426,402,307,65,343,427,403,66,305,341,425,401,63,302,338,422,398,64,303,339,423,399,62,304,340,424,400,665,666,664,662,392,88,332,416,197,333,393,198,86,417,394,199,87,334,418,395,91,196,335,419,396,89,194,336,420,397,90,195,337,421,94,390,203,330,414,391,92,204,331,415,93,389,205,329,413,97,386,202,326,410,95,387,200,327,411,96,388,201,328,412,688,686,685,687,524,255,215,82,440,216,525,441,256,80,526,442,254,217,81,527,258,443,214,85,528,259,444,212,83,529,257,445,213,84,261,522,438,206,77,523,262,439,207,78,260,521,437,208,79,264,518,434,209,76,265,519,435,210,74,263,520,436,211,75,663,661,667,670,356,32,125,380,368,126,357,369,33,381,358,370,34,127,382,359,35,371,124,383,360,36,372,122,384,361,37,373,123,385,30,354,366,131,378,355,31,367,132,379,29,353,365,133,377,26,350,362,130,374,27,351,363,128,375,28,352,364,129,376,676,673,675,674,452,141,48,548,536,49,453,537,142,549,454,538,140,47,550,455,144,539,44,551,456,145,540,45,552,457,143,541,46,553,139,450,534,39,546,451,137,535,40,547,138,449,533,38,545,135,446,530,42,542,136,447,531,43,543,134,448,532,41,544,672,669,671,668,111,168,512,251,320,513,112,321,169,252,110,322,167,514,253,114,164,323,515,250,115,165,324,516,248,113,166,325,517,249,159,117,318,510,242,118,160,319,511,243,158,116,317,509,244,162,120,314,506,245,163,121,315,507,246,161,119,316,508,247,699,697,694,693,596,107,1,639,7,642,643,641,108,640,646,645,109,644,647,650,106,648,649,651,654,104,652,653,655,658,105,656,657,659,98,594,11,2,634,595,99,12,3,635,100,593,13,0,633,101,590,10,5,637,102,591,8,6,638,103,592,9,4,636,701,702,704,703,615,181,476,572,157,477,616,155,179,573,617,156,180,478,574,618,177,153,479,575,619,178,154,480,576,620,176,152,481,577,172,613,148,474,570,614,170,146,475,571,171,612,147,473,569,175,609,151,470,566,173,610,149,471,567,174,611,150,472,568,698,695,696,700,464,288,299,603,57,300,465,58,289,604,466,56,287,301,605,467,284,60,298,606,468,285,61,296,607,469,286,59,297,608,279,462,55,290,601,463,280,53,291,602,278,461,54,292,600,282,458,51,293,597,283,459,52,294,598,281,460,50,295,599,682,680,684,678,584,18,189,627,488,190,585,489,19,628,586,490,17,188,629,587,14,491,192,630,588,15,492,193,631,589,16,493,191,632,24,582,486,187,625,583,25,487,185,626,23,581,485,186,624,20,578,482,183,621,21,579,483,184,622,22,580,484,182,623,683,677,679,681,241,276,500,560,229,501,239,227,277,561,240,228,275,502,562,237,272,225,503,563,238,273,226,504,564,236,274,224,505,565,267,232,220,498,558,230,268,218,499,559,266,231,219,497,557,270,235,223,494,554,271,233,221,495,555,269,234,222,496,556,691,689,692,690 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#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 16:50:03 · history