Equation 677 Database

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Magma b62d5fe26c76…

magma b62d5fe26c76
Size
381
Isomorphism class hash
b62d5fe26c7628538ddb2dd9533b7ddc9b5cbec1afa39f8d8f64ba408c0e4278
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:39:31
Display reorder
380,148,143,298,128,133,138,233,238,228,218,223,213,253,240,245,268,258,263,98,88,93,288,15,14,13,278,12,53,58,48,178,168,173,163,153,158,273,23,28,43,32,38,63,283,68,73,78,83,183,188,193,198,203,208,306,308,307,311,310,309,123,293,118,108,113,103,348,368,333,378,357,343,353,362,338,373,149,144,299,129,134,139,234,239,229,219,224,214,254,244,249,269,259,264,99,89,94,289,19,18,17,279,16,54,59,49,179,169,174,164,154,159,274,24,29,44,33,39,64,284,69,74,79,84,184,189,194,199,204,209,323,322,321,319,318,320,124,294,119,109,114,104,349,369,334,379,359,344,354,363,339,374,146,142,297,127,132,137,231,236,226,215,220,210,252,241,246,267,256,262,96,85,91,285,6,7,1,276,0,50,55,46,176,165,170,161,151,156,272,22,27,42,30,37,61,280,66,71,76,80,180,185,190,196,201,206,312,314,313,317,316,315,120,291,115,106,112,102,345,366,332,375,356,341,350,360,337,371,147,141,295,125,131,136,232,237,227,217,222,212,251,243,248,265,255,260,97,87,92,287,10,11,9,277,8,52,57,47,177,167,172,162,152,157,271,20,26,41,34,36,62,282,67,72,77,82,182,187,192,197,202,207,300,301,302,303,305,304,121,290,116,107,111,100,347,367,330,377,358,342,352,361,336,372,145,140,296,126,130,135,230,235,225,216,221,211,250,242,247,266,257,261,95,86,90,286,5,4,3,275,2,51,56,45,175,166,171,160,150,155,270,21,25,40,31,35,60,281,65,70,75,81,181,186,191,195,200,205,324,326,325,329,328,327,122,292,117,105,110,101,346,365,331,376,355,340,351,364,335,370 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {69} 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, 76): MacNeish's product over GF(4) x GF(19); 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:39:32 · history