Equation 677 Database

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Magma 225c0a2e2da7…

magma 225c0a2e2da7
Size
705
Isomorphism class hash
225c0a2e2da784ab6d0a21b95e51bb010b238b532f6e33be7e786f50f5154abe
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 17:27:01
Display reorder
660,164,167,154,438,74,165,168,72,152,439,166,169,73,153,437,163,170,77,150,434,161,171,75,151,435,162,172,76,149,436,145,173,155,80,429,174,156,78,143,430,175,157,79,144,428,158,176,83,148,432,159,177,81,146,433,160,178,82,147,431,666,661,665,670,264,229,414,43,329,265,230,330,415,44,266,228,331,413,46,263,225,328,410,40,261,226,326,411,38,262,227,327,412,39,405,235,270,320,35,236,271,321,406,36,234,272,322,404,37,269,231,323,408,34,267,232,324,409,32,268,233,325,407,33,686,690,688,685,641,7,606,546,90,642,8,91,607,547,640,6,92,605,545,637,10,93,602,542,638,11,94,603,543,639,9,95,604,544,597,5,632,88,537,3,633,89,598,538,4,631,87,596,536,635,0,84,600,540,636,2,85,601,541,634,1,86,599,539,671,667,668,672,339,462,253,240,277,340,463,278,254,241,338,461,276,252,242,342,458,273,249,239,343,459,274,250,237,341,460,275,251,238,259,453,337,283,246,454,335,284,260,247,452,336,282,258,248,333,456,279,255,245,334,457,280,256,243,332,455,281,257,244,682,673,675,680,450,22,582,510,286,451,23,287,583,511,449,21,285,581,509,446,18,289,578,506,447,19,290,579,507,448,20,288,580,508,573,13,441,292,501,14,442,293,574,502,12,440,291,572,500,444,16,295,576,504,445,17,296,577,505,443,15,294,575,503,669,664,662,663,570,486,426,184,103,571,487,104,427,182,569,485,102,425,183,566,482,106,422,180,567,483,107,423,181,568,484,105,424,179,417,477,561,101,190,478,562,99,418,188,476,560,100,416,189,564,480,97,420,186,565,481,98,421,187,563,479,96,419,185,694,693,695,697,191,653,618,202,213,658,659,214,656,657,192,652,215,617,203,193,649,216,614,204,194,650,217,615,205,195,651,218,616,206,609,644,196,219,207,645,197,220,610,208,643,198,221,608,209,199,647,222,612,210,200,648,223,613,211,201,646,224,611,212,702,703,704,701,534,297,25,114,52,535,654,53,26,655,533,304,51,24,118,530,305,48,28,115,531,306,49,29,116,532,307,50,27,117,31,303,525,58,112,301,526,59,41,113,302,524,57,30,111,528,299,54,45,108,529,300,55,47,109,527,298,56,42,110,698,700,699,696,558,474,402,498,136,559,475,134,403,499,557,473,135,401,497,554,470,132,398,494,555,471,133,399,495,556,472,131,400,496,393,465,549,142,489,466,550,140,394,490,464,548,141,392,488,552,468,138,396,492,553,469,139,397,493,551,467,137,395,491,674,677,676,681,594,522,317,629,71,595,523,69,318,630,593,521,70,319,628,590,518,67,316,625,591,519,68,314,626,592,520,66,315,627,308,513,585,62,620,514,586,60,309,621,512,584,61,310,619,588,516,65,311,623,589,517,63,312,624,587,515,64,313,622,679,684,678,683,384,353,371,357,128,385,354,129,372,358,383,355,130,373,356,380,352,127,370,360,381,350,125,368,361,382,351,126,369,359,377,344,390,119,363,345,391,120,378,364,346,389,121,379,362,386,347,122,376,366,387,348,123,374,367,388,349,124,375,365,689,692,691,687 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#5751a2f21b762bdcbb8d7ca8109ff664440cd913db63bda4230c3be52dd8f5e2, 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 17:27:02 · history