Equation 677 Database

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Magma 4d2c9e7627f6…

magma 4d2c9e7627f6
Size
381
Isomorphism class hash
4d2c9e7627f6aa620cef6306ebd5ab412f172437199ebfe754ad36da6215a92f
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 23:39:27
Display reorder
380,136,145,141,130,121,125,170,176,165,156,161,150,310,311,309,307,308,306,101,105,96,291,115,110,14,6,296,17,15,16,242,29,30,31,1,0,277,262,267,258,247,254,239,289,234,224,229,219,80,86,90,71,76,280,191,186,181,200,195,205,274,69,64,54,59,214,349,361,330,340,339,356,351,370,367,377,138,148,143,133,123,128,173,178,168,158,163,153,317,315,316,314,312,313,103,108,98,293,118,113,35,36,298,32,33,34,243,37,38,39,7,8,278,263,268,257,245,251,237,287,232,222,227,217,82,88,93,73,78,283,193,188,183,203,198,208,272,67,62,52,57,212,347,363,333,343,337,357,353,373,368,378,137,147,142,132,122,127,172,177,167,157,162,152,304,305,303,300,302,301,102,107,97,292,117,112,27,28,297,24,25,26,240,21,22,20,18,19,276,260,265,256,248,253,235,285,230,221,226,216,84,87,92,72,77,282,190,185,180,201,196,206,270,66,61,50,55,210,345,362,331,342,336,355,352,372,365,375,135,146,140,131,120,126,171,175,166,155,160,151,321,322,323,318,319,320,100,106,95,290,116,111,12,13,295,9,10,11,241,5,4,2,3,23,275,261,266,255,249,252,236,286,231,220,225,215,81,85,91,70,75,281,192,187,182,202,197,207,271,65,60,51,56,211,346,360,332,341,335,358,350,371,366,376,139,149,144,134,124,129,174,179,169,159,164,154,326,324,325,329,327,328,104,109,99,294,119,114,43,44,299,41,42,40,244,47,48,49,45,46,279,264,269,259,246,250,238,288,233,223,228,218,83,89,94,74,79,284,194,189,184,204,199,209,273,68,63,53,58,213,348,364,334,344,338,359,354,374,369,379 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 = {68} 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 23:39:28 · history