Equation 677 Database

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Magma bfd662e62981…

magma bfd662e62981
Size
381
Isomorphism class hash
bfd662e62981fe484ffeb1315ac6ed1077809901ac3a7e9fea7f51b6b84c3eb2
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 23:46:07
Display reorder
380,221,215,226,231,236,210,118,119,114,115,116,117,104,105,106,107,102,103,113,108,109,110,111,112,100,101,96,97,98,99,301,300,302,303,304,305,151,156,161,166,170,175,91,92,93,94,95,90,256,261,265,241,246,251,292,297,272,275,280,285,185,206,191,196,201,180,341,375,355,337,333,371,340,331,364,365,224,219,229,233,238,213,129,130,131,126,127,128,148,149,144,145,146,147,121,122,123,124,125,120,140,141,142,143,138,139,306,307,308,309,310,311,154,158,163,168,173,179,132,133,134,135,136,137,259,263,268,243,249,254,293,298,273,279,284,288,189,208,194,199,203,183,358,379,342,332,330,374,344,356,360,369,220,216,225,230,235,211,75,76,77,72,73,74,63,64,65,60,61,62,67,68,69,70,71,66,86,87,88,89,84,85,326,327,328,329,324,325,150,155,160,165,171,176,78,79,80,81,82,83,255,260,266,240,245,250,291,295,270,277,281,286,186,205,190,195,200,181,357,376,336,353,346,370,354,345,362,366,223,218,228,234,239,214,52,53,48,49,50,51,38,39,40,41,36,37,47,42,43,44,45,46,54,55,56,57,58,59,314,315,316,317,312,313,153,159,164,169,174,178,4,5,1,0,2,3,258,264,269,244,248,253,294,299,274,278,283,289,188,209,193,198,204,184,359,378,352,351,339,373,343,338,363,368,222,217,227,232,237,212,14,15,16,17,12,13,27,28,29,24,25,26,31,32,33,34,35,30,10,11,6,7,8,9,319,320,321,322,323,318,152,157,162,167,172,177,21,22,23,18,19,20,257,262,267,242,247,252,290,296,271,276,282,287,187,207,192,197,202,182,334,377,335,347,348,372,350,349,361,367 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, 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 23:46:08 · history