Equation 677 Database

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Magma deaaef9d40df…

magma deaaef9d40df
Size
705
Isomorphism class hash
deaaef9d40df0bd8cb43a813493a48e48845838a279e3f4e70d61a98d01c7927
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 19:08:16
Display reorder
660,164,375,188,182,338,376,339,165,189,183,340,374,166,190,184,371,337,163,187,181,335,372,161,185,179,336,373,162,186,180,344,381,170,194,173,345,382,171,195,174,175,346,380,172,196,377,343,169,193,176,191,378,341,167,177,379,342,168,192,178,671,668,672,663,471,15,287,283,231,16,232,472,288,281,230,17,470,289,282,14,227,467,290,286,228,12,468,291,284,229,13,469,292,285,222,21,477,293,278,223,22,478,294,279,280,221,23,476,295,20,225,473,296,277,297,18,226,474,275,19,224,475,298,276,687,689,686,688,210,523,363,559,127,524,125,211,364,560,126,522,209,362,558,519,130,213,359,555,128,520,214,360,556,129,521,212,361,557,133,529,216,369,565,131,530,217,370,566,564,132,528,215,368,525,136,219,365,561,366,526,134,220,562,527,135,218,367,563,670,661,662,669,46,303,547,240,80,304,81,44,548,241,82,302,45,546,239,299,79,42,543,243,77,300,43,544,244,78,301,41,545,242,86,309,52,553,238,87,310,50,554,236,237,88,308,51,552,305,85,48,549,234,550,306,83,49,235,307,84,47,551,233,673,682,680,674,483,399,459,423,256,400,254,484,460,424,255,398,482,458,422,395,252,479,455,419,253,396,480,456,420,251,397,481,457,421,247,405,489,465,429,245,406,490,466,430,428,246,404,488,464,401,250,485,461,425,462,402,248,486,426,403,249,487,463,427,665,666,667,664,535,205,447,154,351,203,352,536,448,152,350,204,534,446,153,208,347,531,443,150,348,206,532,444,151,349,207,533,445,149,357,200,541,453,160,358,201,542,454,158,159,356,202,540,452,199,353,537,449,156,450,197,354,538,157,198,355,539,451,155,693,695,696,694,571,491,24,500,72,634,73,635,633,632,71,492,570,25,499,494,75,567,27,496,76,495,568,28,497,74,493,569,26,498,70,652,655,654,653,68,656,659,658,657,649,69,648,651,650,636,66,639,638,637,642,640,67,643,641,645,65,647,646,644,701,703,704,702,504,600,576,257,32,601,33,505,577,258,34,599,506,575,259,596,31,503,572,260,29,597,501,573,261,30,598,502,574,262,38,606,628,582,629,39,607,630,583,631,627,40,605,626,581,602,37,620,578,621,579,603,35,622,623,604,36,624,580,625,699,697,700,698,612,511,327,588,54,512,55,613,328,589,53,510,611,326,587,507,57,608,323,584,58,508,609,324,585,56,509,610,325,586,60,517,618,333,594,61,518,619,334,595,593,59,516,617,332,513,63,614,329,590,330,514,64,615,591,515,62,616,331,592,683,675,684,679,435,387,113,411,265,388,263,436,114,412,264,386,434,115,410,383,268,431,116,407,266,384,432,117,408,267,385,433,118,409,271,393,441,119,417,269,394,442,120,418,416,270,392,440,121,389,274,437,122,413,123,390,272,438,414,391,273,439,124,415,677,681,678,676,111,95,139,313,11,96,9,112,137,311,10,97,110,138,312,98,7,107,142,316,8,99,108,140,314,6,100,109,141,315,2,93,102,145,319,1,94,103,143,317,318,0,92,101,144,89,5,105,148,322,146,90,3,106,320,91,4,104,147,321,690,691,685,692 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#87aba77d55a93960597d69a42bda986d959be94fa8d2c920629e2ba026b38a72, 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 19:08:17 · history