Equation 677 Database

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Magma 6768f4bf4041…

magma 6768f4bf4041
Size
705
Isomorphism class hash
6768f4bf404163a2d702ba1b4baac0ffa022deb104842a9a3be17af4bed8853b
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 17:20:03
Display reorder
660,333,337,229,380,349,334,338,230,378,350,335,336,228,379,348,332,340,232,383,352,233,341,330,381,353,339,331,231,382,351,324,343,235,375,355,325,344,236,376,356,326,342,234,377,354,346,327,238,374,358,347,328,239,372,359,345,329,237,373,357,664,670,668,666,31,491,175,563,207,32,489,176,561,208,30,490,174,562,209,34,487,178,559,206,179,488,35,560,204,486,33,177,558,205,29,482,173,554,213,27,480,171,552,214,28,481,172,553,215,485,25,169,557,212,483,26,170,555,210,484,24,168,556,211,689,690,686,688,599,632,255,455,37,597,630,256,453,38,598,631,257,454,36,595,628,254,451,40,252,629,596,452,41,627,594,253,450,39,590,623,261,446,43,588,621,262,444,44,589,622,263,445,42,626,593,260,449,46,624,591,258,447,47,625,592,259,448,45,663,662,672,671,197,8,226,180,431,195,6,227,181,429,196,7,225,182,430,193,11,222,183,427,223,9,194,184,428,10,192,224,185,426,203,3,217,186,422,201,4,218,187,420,202,5,216,188,421,2,199,220,189,425,1,200,221,190,423,0,198,219,191,424,673,676,678,674,407,575,103,503,527,405,573,104,501,525,406,574,102,502,526,403,571,106,499,523,107,572,404,500,524,570,402,105,498,522,398,566,109,494,518,396,564,110,492,516,397,565,108,493,517,569,401,112,497,521,567,399,113,495,519,568,400,111,496,520,665,667,669,661,395,479,368,551,248,393,477,366,549,246,394,478,367,550,247,391,475,371,547,251,369,476,392,548,249,474,390,370,546,250,386,470,363,542,243,384,468,364,540,244,385,469,365,541,245,473,389,362,545,242,471,387,360,543,240,472,388,361,544,241,696,693,695,694,656,659,74,657,658,650,651,72,648,649,652,655,73,653,654,606,640,77,84,100,75,641,607,85,101,639,608,76,86,99,601,635,80,91,95,602,633,78,92,93,600,634,79,90,94,638,604,83,87,98,636,605,81,88,96,637,603,82,89,97,701,703,704,702,121,647,56,149,646,122,642,54,147,643,120,644,55,148,645,124,132,59,145,135,57,133,125,146,136,134,123,58,144,137,119,127,51,155,138,117,128,52,153,139,118,126,53,154,140,130,115,50,151,141,131,116,48,152,142,129,114,49,150,143,698,699,700,697,467,419,316,443,539,465,417,317,441,537,466,418,315,442,538,463,415,312,439,535,313,416,464,440,536,414,462,314,438,534,458,410,322,434,530,456,408,323,432,528,457,409,321,433,529,413,461,318,437,533,411,459,319,435,531,412,460,320,436,532,677,682,675,679,161,515,23,587,620,159,513,21,585,618,160,514,22,586,619,157,511,19,583,616,20,512,158,584,617,510,156,18,582,615,167,506,14,578,611,165,504,12,576,609,166,505,13,577,610,509,163,17,581,614,507,164,15,579,612,508,162,16,580,613,683,684,680,681,310,266,64,292,281,311,264,65,293,279,309,265,63,291,280,306,269,60,288,277,61,267,307,289,278,268,308,62,290,276,301,272,70,298,287,302,270,71,299,285,300,271,69,297,286,275,304,66,294,283,273,305,67,295,284,274,303,68,296,282,687,691,692,685 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#4ddcb3732d8cead11c348e4cf9e2318d25466469e5bf7b5d48d8ea06dbb2e5f3, 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 17:20:04 · history