Equation 677 Database

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Magma 5efa7656e0fc…

magma 5efa7656e0fc
Size
705
Isomorphism class hash
5efa7656e0fca77a7f6ba6d95cdba658ad2b997f8c76724d1803c26a6d8aed1a
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 16:33:53
Display reorder
660,422,121,380,518,494,381,423,519,495,122,379,120,421,517,493,376,418,124,514,490,377,419,125,515,491,378,420,123,516,492,127,524,428,371,500,128,525,429,372,501,126,523,427,370,499,520,130,424,374,496,521,131,425,375,497,373,522,129,426,498,667,664,668,672,482,624,29,506,4,27,483,507,5,625,28,623,481,505,3,25,478,620,502,1,26,479,621,503,0,24,480,622,504,2,630,512,488,35,10,631,513,489,33,11,629,511,487,34,9,508,626,484,31,6,509,627,485,32,7,30,510,628,486,8,690,687,688,691,458,148,268,325,315,269,459,326,313,149,270,147,457,327,314,271,454,144,324,311,272,455,145,322,312,273,456,146,323,310,154,331,464,266,321,155,332,465,267,319,153,333,463,265,320,330,150,460,262,317,328,151,461,263,318,264,329,152,462,316,661,666,663,665,570,446,93,571,400,94,572,573,401,447,95,445,568,569,402,92,562,442,563,403,90,564,443,565,404,91,567,444,566,405,452,582,583,84,398,453,585,584,85,399,451,580,581,86,397,574,448,575,87,394,576,449,577,88,395,89,579,450,578,396,674,682,681,677,636,530,227,410,554,228,637,411,555,531,226,529,635,409,553,230,632,526,406,550,231,633,527,407,551,229,634,528,408,552,536,416,642,233,560,537,417,643,234,561,535,415,641,232,559,412,532,638,236,556,413,533,639,237,557,235,414,534,640,558,670,671,662,669,137,299,383,295,281,384,135,296,282,300,382,298,136,297,280,386,133,302,294,284,387,134,303,292,285,385,132,301,293,283,305,286,143,389,279,306,287,141,390,277,304,288,142,388,278,289,308,139,392,275,290,309,140,393,276,391,291,307,138,274,697,696,695,693,205,200,219,613,590,217,206,614,591,201,218,202,204,612,589,215,208,199,609,586,216,209,197,610,587,214,207,198,611,588,192,619,203,225,596,659,658,657,223,656,193,618,210,224,595,615,194,211,221,592,616,195,212,222,593,220,617,196,213,594,701,703,704,702,37,601,243,542,59,241,38,543,57,602,242,600,36,541,58,239,40,597,538,55,240,41,598,539,56,238,39,599,540,54,607,548,43,249,50,608,549,44,247,48,606,547,42,248,49,544,603,46,245,53,545,604,47,246,51,244,546,605,45,52,699,700,694,698,368,353,21,185,174,22,369,183,175,354,23,352,367,184,176,20,364,356,181,177,18,365,357,182,178,19,366,355,180,179,351,191,359,12,172,349,189,360,13,173,350,190,358,14,171,187,347,362,15,168,188,348,363,16,169,17,186,346,361,170,679,678,680,684,648,75,255,60,434,253,649,61,435,76,254,77,647,62,433,251,644,74,63,430,252,645,72,64,431,250,646,73,65,432,81,66,654,261,440,82,67,655,259,441,83,68,653,260,439,69,80,650,257,436,70,78,651,258,437,256,71,79,652,438,676,683,675,673,108,98,161,334,470,159,109,335,471,96,160,97,110,336,469,157,111,101,337,466,158,112,99,338,467,156,113,100,339,468,104,340,114,167,476,102,341,115,165,477,103,342,116,166,475,343,107,117,163,472,344,105,118,164,473,162,345,106,119,474,686,689,692,685 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#3519a427d5ae28e51e8dce355af6af1aa210384ac7088475411fc50e96b55163, 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 16:33:54 · history