Equation 677 Database

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Magma 3e2464e02995…

magma 3e2464e02995
Size
707
Isomorphism class hash
3e2464e029956296b68c81c55b68dbbe86c99f5bd1a4ee3eaade3edcb22ba60d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 08:08:41
Display reorder
302,300,301,303,304,305,656,195,197,196,192,193,194,153,155,154,151,152,150,163,162,164,165,166,167,187,186,188,189,190,191,184,183,185,180,181,182,289,290,291,292,293,288,15,17,16,14,12,13,9,11,10,7,8,6,294,295,296,298,299,297,156,158,157,161,159,160,473,472,468,469,470,471,465,464,466,467,462,463,602,600,603,604,605,601,306,307,308,309,310,311,521,520,516,517,518,519,514,513,515,510,511,512,479,478,474,475,476,477,459,458,460,461,456,457,508,507,509,504,505,506,484,483,485,480,481,482,627,610,626,609,625,606,642,615,634,641,703,697,704,695,706,698,696,658,705,694,82,81,83,79,80,78,24,26,25,28,29,27,261,263,262,260,259,258,120,122,121,125,123,124,179,178,177,175,176,174,49,48,50,51,52,53,148,147,149,144,145,146,136,135,137,134,132,133,240,242,241,243,244,245,143,142,141,139,140,138,431,430,426,427,428,429,419,418,414,415,416,417,591,590,592,593,589,588,546,551,547,548,549,550,586,585,587,583,582,584,566,565,567,568,569,564,563,562,558,559,560,561,347,346,342,343,344,345,598,597,599,595,594,596,523,522,524,525,526,527,650,646,654,635,655,631,645,620,639,640,657,661,664,667,672,659,674,675,669,679,45,47,46,42,43,44,5,4,3,1,0,2,118,117,119,114,115,116,127,126,128,129,130,131,38,37,36,40,41,39,67,66,68,69,70,71,111,113,112,110,108,109,92,91,90,93,94,95,238,237,239,235,236,234,219,221,220,218,216,217,554,553,555,556,557,552,385,384,386,387,388,389,412,411,413,408,409,410,392,391,393,394,395,390,500,499,501,502,503,498,400,399,401,396,397,398,337,336,338,339,340,341,332,331,333,334,335,330,532,531,533,528,529,530,577,576,578,579,580,581,648,644,647,638,649,630,633,619,632,616,663,660,662,689,683,691,685,693,687,681,286,285,287,282,284,283,224,223,222,225,226,227,277,278,276,281,279,280,96,98,97,101,99,100,74,73,72,76,77,75,88,87,89,84,85,86,271,272,270,275,273,274,268,267,269,266,265,264,30,32,31,33,34,35,203,202,201,199,200,198,538,537,539,534,535,536,350,349,351,352,353,348,433,432,434,435,436,437,423,422,424,425,420,421,445,444,446,447,448,449,574,573,575,570,571,572,440,439,441,442,443,438,491,490,486,487,488,489,368,367,369,370,371,366,376,375,377,372,373,374,653,643,651,628,652,636,637,617,629,614,668,666,665,688,684,680,690,686,682,692,23,22,21,20,18,19,247,246,248,251,249,250,170,169,168,172,173,171,61,60,62,63,64,65,257,256,255,253,254,252,56,55,54,58,59,57,232,231,233,228,229,230,102,104,103,106,107,105,206,205,204,209,207,208,215,214,213,211,212,210,381,380,382,383,378,379,402,407,403,404,405,406,364,363,365,360,361,362,317,316,312,313,314,315,355,354,356,357,358,359,453,452,454,455,450,451,323,322,318,319,320,321,494,493,495,496,497,492,329,328,324,325,326,327,542,541,543,544,545,540,622,611,624,607,623,608,621,612,618,613,699,671,700,676,702,673,677,670,701,678 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = {36, 37, 38, 39, 40, 41, 136} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-06 08:08:42 · history