Equation 677 Database

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Magma 86de7f1c63b6…

magma 86de7f1c63b6
Size
381
Isomorphism class hash
86de7f1c63b6a576bc8b0e41488751e849018884eae9d196ee0bbdb2cc1e06ba
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 23:39:43
Display reorder
380,76,218,77,78,11,12,166,171,176,150,155,160,72,71,75,213,73,74,126,130,120,141,146,136,314,312,313,317,315,316,261,250,256,246,236,241,228,87,88,86,84,85,203,208,198,188,193,183,81,79,80,83,82,223,89,91,90,292,232,92,280,296,287,276,267,271,333,361,338,355,348,365,370,343,353,376,34,215,35,33,31,32,167,172,177,152,157,162,68,66,67,212,69,70,127,131,122,142,147,137,307,308,306,310,311,309,262,252,257,247,237,242,227,43,44,45,2,0,202,207,197,187,192,182,17,42,18,15,16,221,14,13,93,291,230,27,282,295,285,275,265,274,332,362,337,356,346,367,372,340,352,377,36,216,3,4,5,6,165,170,175,151,156,161,58,59,65,211,56,57,125,134,121,140,145,135,320,318,319,323,321,322,260,251,255,245,235,240,226,10,9,8,26,7,200,205,195,186,191,180,37,38,39,40,41,220,29,28,30,290,231,1,281,297,286,277,266,270,330,360,336,358,345,366,371,341,351,375,48,217,49,50,46,47,168,173,178,153,158,163,62,60,61,210,63,64,128,132,123,143,148,138,326,324,325,329,327,328,263,253,258,248,238,243,225,24,25,23,21,22,201,206,196,185,190,181,53,51,52,55,54,222,94,95,97,293,233,96,283,298,288,278,268,272,331,363,335,357,347,368,373,342,350,378,103,219,104,105,20,19,169,174,179,154,159,164,99,98,102,214,100,101,129,133,124,144,149,139,301,300,302,303,304,305,264,254,259,249,239,244,229,114,115,113,111,112,204,209,199,189,194,184,108,106,107,110,109,224,116,117,119,294,234,118,284,299,289,279,269,273,334,364,339,359,349,369,374,344,354,379 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 = {72} 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 23:39:44 · history