Equation 677 Database

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Magma b7df4c4aa24c…

magma b7df4c4aa24c
Size
705
Isomorphism class hash
b7df4c4aa24c42e9e5bf30bb8960c5cd43649d9cce0776a28d4d3d2fd431c2bb
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 21:52:22
Display reorder
660,286,176,431,299,235,287,236,174,429,297,175,234,285,430,298,289,172,231,427,302,290,173,232,428,300,288,171,233,426,301,167,226,437,292,305,227,165,435,293,303,291,225,166,436,304,170,229,433,295,308,168,230,434,296,306,169,228,432,294,307,672,669,667,663,443,26,395,105,122,441,120,27,393,106,28,121,442,394,107,439,25,118,391,108,440,23,119,392,109,438,24,117,390,110,32,128,401,449,111,126,33,399,447,112,448,127,34,400,113,31,124,397,445,114,29,125,398,446,115,30,123,396,444,116,685,687,691,686,131,200,254,419,491,129,489,198,252,417,199,490,130,253,418,134,196,487,250,415,132,197,488,251,416,133,195,486,249,414,191,497,260,137,425,495,189,258,135,423,136,496,190,259,424,194,493,256,140,421,192,494,257,138,422,193,492,255,139,420,665,670,661,668,374,46,364,479,536,372,534,44,365,477,45,535,373,363,478,370,42,532,367,475,371,43,533,368,476,369,41,531,366,474,37,542,362,380,485,540,35,360,378,483,379,541,36,361,484,40,538,358,376,481,38,539,359,377,482,39,537,357,375,480,679,674,676,682,158,334,455,629,512,156,510,335,453,627,333,511,157,454,628,154,337,508,451,625,155,338,509,452,626,153,336,507,450,624,340,518,461,164,635,516,341,459,162,633,163,517,339,460,634,343,514,457,160,631,344,515,458,161,632,342,513,456,159,630,666,662,671,664,572,238,326,178,316,570,317,239,324,179,237,315,571,325,177,568,241,319,322,181,569,242,320,323,182,567,240,318,321,180,244,314,332,578,184,312,245,330,576,185,577,313,243,331,183,247,310,328,574,187,248,311,329,575,188,246,309,327,573,186,698,699,693,694,7,13,584,386,502,56,503,11,582,384,12,501,58,583,385,60,16,498,580,382,63,14,499,581,383,66,15,500,579,381,19,658,659,657,656,651,17,650,649,648,653,654,18,655,652,22,504,586,10,388,20,505,587,8,389,21,506,585,9,387,703,701,702,704,548,85,76,593,350,546,348,86,77,591,84,349,547,75,592,544,81,346,79,589,545,82,347,80,590,543,83,345,78,588,91,356,74,554,599,354,92,72,552,597,553,355,90,73,598,87,352,70,550,595,88,353,71,551,596,89,351,69,549,594,695,697,700,696,605,274,218,407,560,603,558,275,216,405,273,559,604,217,406,601,277,556,214,403,602,278,557,215,404,600,276,555,213,402,280,566,224,611,413,564,281,222,609,411,610,565,279,223,412,283,562,220,607,409,284,563,221,608,410,282,561,219,606,408,680,681,675,684,641,0,103,50,524,639,522,2,104,51,3,523,640,102,52,637,4,520,99,49,638,5,521,100,47,636,6,519,101,48,1,530,94,647,59,528,54,95,645,53,646,529,57,93,55,61,526,97,643,68,64,527,98,644,62,67,525,96,642,65,678,683,677,673,152,265,617,467,209,150,207,266,615,465,264,208,151,616,466,148,261,212,613,463,149,262,210,614,464,147,263,211,612,462,271,204,623,143,473,205,272,621,141,471,142,206,270,622,472,267,203,619,146,469,268,201,620,144,470,269,202,618,145,468,688,689,690,692 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#f80d3e42bb36c9de3f16a7272ddaae8a1c868ead8083a2f830ed5472d041fc61, 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 21:52:23 · history