Equation 677 Database

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Magma 3ba396f61545…

magma 3ba396f61545
Size
705
Isomorphism class hash
3ba396f6154592923c53414afc81054943dd081a914db2c8199b0a54aaa66456
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 20:34:16
Display reorder
660,26,386,482,185,195,24,384,480,183,196,25,385,481,184,197,29,389,485,181,194,27,387,483,182,192,28,388,484,180,193,32,392,488,191,201,30,390,486,189,202,31,391,487,190,203,395,35,491,187,200,393,33,489,188,198,394,34,490,186,199,671,661,663,667,367,494,434,308,323,368,492,432,306,321,366,493,433,307,322,370,497,437,311,319,371,495,435,309,320,369,496,436,310,318,365,500,440,303,314,363,498,438,304,312,364,499,439,305,313,503,361,443,302,317,501,362,441,300,315,502,360,442,301,316,690,689,687,686,219,446,3,578,470,220,444,4,576,468,221,445,5,577,469,218,449,2,581,473,216,447,1,579,471,217,448,0,580,472,225,452,9,584,476,226,450,10,582,474,227,451,11,583,475,455,224,8,587,479,453,222,6,585,477,454,223,7,586,478,672,666,665,670,96,338,530,374,334,97,336,528,372,335,98,337,529,373,333,99,341,533,377,330,100,339,531,375,331,101,340,532,376,332,102,344,536,380,325,103,342,534,378,326,104,343,535,379,324,347,105,539,383,328,345,106,537,381,329,346,107,538,382,327,676,673,674,680,58,293,50,272,287,61,291,53,270,285,55,292,47,271,286,67,289,38,275,283,70,290,41,273,284,63,288,44,274,282,52,299,68,267,278,46,297,71,268,276,49,298,65,269,277,295,40,56,266,281,296,42,59,264,279,294,36,62,265,280,669,662,664,668,130,211,458,77,566,131,212,456,75,564,129,210,457,76,565,126,214,461,73,569,127,215,459,74,567,128,213,460,72,568,121,209,464,83,572,122,207,462,81,570,120,208,463,82,571,205,124,467,79,575,206,125,465,80,573,204,123,466,78,574,693,698,696,694,162,622,623,621,620,163,615,614,613,612,164,618,619,617,616,165,634,635,633,632,166,627,626,624,625,167,630,631,629,628,160,646,647,644,645,161,638,639,636,637,159,642,643,640,641,658,156,659,656,657,651,157,650,649,648,654,158,655,652,653,701,702,704,703,355,87,542,593,592,356,88,540,588,589,354,89,541,591,590,358,86,545,599,598,359,84,543,594,595,357,85,544,596,597,353,93,548,605,604,351,94,546,600,601,352,95,547,603,602,92,349,551,611,610,90,350,549,606,607,91,348,550,609,608,699,700,695,697,114,174,137,18,554,115,175,135,19,552,116,176,136,20,553,117,177,133,21,557,118,178,134,22,555,119,179,132,23,556,112,172,143,16,560,113,173,141,17,558,111,171,142,15,559,168,108,139,12,563,169,109,140,13,561,170,110,138,14,562,684,682,681,678,427,396,410,146,518,428,397,408,144,516,426,398,409,145,517,430,399,413,149,521,431,400,411,147,519,429,401,412,148,520,425,402,416,152,524,423,403,414,150,522,424,404,415,151,523,405,421,419,155,527,406,422,417,153,525,407,420,418,154,526,683,679,675,677,48,240,253,506,228,51,241,254,504,229,45,242,252,505,230,37,243,256,509,231,39,244,257,507,232,43,245,255,508,233,66,246,259,512,234,69,247,260,510,235,64,248,258,511,236,249,54,262,515,237,250,57,263,513,238,251,60,261,514,239,688,685,692,691 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, 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 20:34:17 · history