Equation 677 Database

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Magma 7f0bd0b6b91d…

magma 7f0bd0b6b91d
Size
705
Isomorphism class hash
7f0bd0b6b91dc61ef70a4b1d791b1aa8bd00b9fe327f0013632ff09ea99e0e8c
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 20:32:32
Display reorder
704,393,525,533,550,394,526,534,548,392,524,535,549,389,521,536,546,390,522,537,547,391,523,538,545,384,516,531,541,385,517,532,539,383,515,530,540,519,387,527,544,520,388,528,542,386,518,529,543,510,511,509,513,514,512,508,506,503,504,505,507,662,661,663,660,119,177,186,152,120,178,187,153,121,176,185,154,122,173,189,151,123,174,190,149,124,175,188,150,125,168,184,143,126,169,182,144,127,167,183,145,171,128,180,146,172,129,181,147,130,170,179,148,156,157,155,159,160,158,162,163,164,165,166,161,688,690,689,691,557,435,401,418,558,436,402,416,559,434,403,417,560,431,404,414,561,432,405,415,562,433,406,413,555,441,399,409,556,442,400,407,554,440,398,408,437,551,395,412,438,552,396,410,553,439,397,411,421,419,420,424,422,423,427,425,429,430,428,426,668,670,669,671,39,202,204,219,40,200,205,220,38,201,203,218,35,198,207,215,36,199,208,216,37,197,206,217,45,193,210,225,46,191,211,226,44,192,209,224,196,41,213,221,194,42,214,222,43,195,212,223,229,227,228,232,230,231,235,233,237,238,236,234,676,679,677,678,15,279,242,258,16,280,243,259,17,278,244,257,14,275,241,261,12,276,239,262,13,277,240,260,21,285,248,256,22,286,249,254,23,284,250,255,281,20,247,252,282,18,245,253,19,283,246,251,266,267,268,265,263,264,272,273,270,271,269,274,664,667,665,666,656,659,658,657,648,651,650,649,652,655,654,653,640,643,642,641,645,647,646,644,636,639,638,637,620,623,622,621,612,615,614,613,616,619,618,617,635,633,634,632,627,625,626,624,629,631,630,628,28,26,27,24,611,25,34,32,29,30,31,33,695,693,694,692,55,98,65,81,53,99,66,82,54,100,67,80,58,97,68,77,56,95,69,78,57,96,70,79,50,104,63,72,51,105,64,73,52,106,62,71,103,49,59,75,101,47,60,76,48,102,61,74,91,89,90,94,92,93,86,87,84,85,83,88,703,701,702,700,7,292,303,312,8,290,304,313,6,291,302,311,10,288,299,315,11,289,300,316,9,287,301,314,5,298,309,318,3,296,310,319,4,297,308,317,294,0,305,321,295,2,306,322,1,293,307,320,327,328,326,323,324,325,333,334,331,329,330,332,699,697,698,696,108,456,470,487,109,457,471,485,107,455,472,486,111,459,469,490,112,460,467,488,110,458,468,489,114,462,476,482,115,463,477,483,113,461,478,484,465,117,475,481,466,118,473,479,116,464,474,480,497,498,499,500,501,502,495,496,493,491,492,494,672,674,673,675,132,381,340,351,133,382,338,352,131,380,339,350,135,377,336,347,136,378,337,348,134,379,335,349,138,372,346,357,139,373,344,358,137,371,345,356,375,141,342,353,376,142,343,354,140,374,341,355,360,361,359,363,364,362,366,367,368,369,370,365,681,683,682,680,452,589,608,565,453,587,609,563,454,588,610,564,451,592,607,568,449,590,605,566,450,591,606,567,443,595,599,571,444,593,600,569,445,594,601,570,598,446,602,574,596,447,603,572,448,597,604,573,585,586,584,581,582,583,576,577,578,579,580,575,686,685,687,684 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, 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 20:32:33 · history