Equation 677 Database

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Magma 567dfe3c3cd6…

magma 567dfe3c3cd6
Size
595
Isomorphism class hash
567dfe3c3cd63a976246de60b5f41d87f2d128baa2ad112df1ab8ae15d3b7239
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 14:06:58
Display reorder
127,126,128,129,124,125,345,344,343,348,346,347,329,328,330,325,326,327,332,331,333,335,336,334,323,322,324,321,319,320,521,533,527,512,559,183,182,184,185,180,181,229,230,231,232,233,228,145,144,146,147,148,149,264,269,265,266,267,268,194,193,195,196,197,192,256,255,257,252,253,254,81,80,76,77,78,79,28,27,29,24,25,26,4,3,5,1,0,2,6,11,7,8,9,10,377,376,375,378,379,380,404,403,405,400,402,401,350,349,368,352,353,351,309,311,310,307,308,306,481,482,509,508,479,480,357,472,437,474,438,473,530,515,525,528,524,529,585,574,583,581,547,549,563,545,544,571,158,157,159,160,161,156,278,279,280,281,276,277,135,134,130,131,132,133,22,21,23,18,19,20,13,12,14,15,16,17,117,116,112,113,114,115,52,51,53,48,49,50,250,249,251,246,247,248,236,235,237,238,239,234,45,44,46,47,42,43,446,447,387,486,499,485,492,501,493,489,490,491,506,468,500,467,435,436,483,445,444,443,453,452,409,411,410,408,407,406,358,477,440,476,439,475,542,532,540,541,514,535,562,554,555,588,589,570,591,564,594,565,166,165,167,162,163,164,95,96,97,98,99,94,70,69,71,66,67,68,54,59,55,56,57,58,245,244,240,241,242,243,63,62,64,65,60,61,107,106,108,109,110,111,190,189,191,186,187,188,274,273,275,270,271,272,104,103,105,100,101,102,362,364,363,360,361,359,412,413,414,416,417,415,370,369,371,373,374,372,316,318,317,314,315,313,466,484,505,354,504,465,469,355,470,507,471,356,536,537,518,517,534,519,561,582,548,586,573,572,552,553,587,566,38,37,39,40,41,36,122,123,118,119,120,121,174,179,175,176,177,178,206,205,207,208,209,204,217,216,218,219,220,221,87,86,82,83,84,85,151,150,152,153,154,155,89,88,90,91,92,93,287,286,282,283,284,285,292,291,293,288,289,290,478,442,441,365,366,367,395,396,394,397,398,399,388,390,389,391,392,448,451,488,393,487,450,449,338,337,339,340,341,342,422,420,502,498,503,421,531,526,523,522,543,516,576,579,550,557,556,578,568,546,590,551,258,263,259,260,261,262,171,172,173,168,169,170,137,136,138,139,140,141,222,227,223,224,225,226,31,30,32,33,34,35,295,294,296,297,298,299,302,301,303,304,305,300,143,142,72,73,74,75,200,199,201,202,203,198,215,214,210,211,212,213,464,433,434,432,431,463,494,455,456,419,454,497,424,423,425,427,428,426,459,496,418,495,457,458,381,383,382,386,384,385,312,462,430,461,429,460,539,538,520,513,510,511,580,569,592,567,558,593,560,577,575,584 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, M = the submagma generated by {30, 72} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 14:06:59 · history