Equation 677 Database

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Magma d21c9c3558e1…

magma d21c9c3558e1
Size
381
Isomorphism class hash
d21c9c3558e107e471b026044a7e8f4cdd05852c23b2124f5e70187169333b98
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 23:23:21
Display reorder
380,139,99,253,307,74,189,279,8,229,164,306,69,199,249,289,134,4,109,224,159,19,264,174,214,59,310,236,124,84,149,24,269,179,204,64,311,244,114,89,154,49,39,44,34,29,284,219,194,79,104,129,294,308,259,169,14,274,184,209,54,309,231,119,94,144,299,379,354,344,339,364,334,369,349,359,374,138,98,252,327,73,188,278,7,228,163,329,68,198,248,288,133,3,108,223,158,18,263,173,213,58,324,239,123,83,148,23,268,178,203,63,325,243,113,88,153,48,38,43,33,28,283,218,193,78,103,128,293,328,258,168,13,273,183,208,53,326,234,118,93,143,298,378,353,343,338,363,333,368,348,358,373,135,96,250,322,70,185,275,5,226,161,321,65,195,247,285,130,0,106,221,156,15,260,171,210,56,319,237,120,81,146,20,265,176,200,61,320,241,110,86,151,46,36,41,30,26,280,216,190,75,101,125,290,323,257,166,10,271,180,205,50,318,232,115,90,140,295,375,351,341,335,361,330,365,345,355,371,137,97,254,313,72,187,277,6,227,162,312,67,197,245,287,132,2,107,222,157,17,261,172,212,57,316,235,122,82,147,22,266,177,202,62,317,240,112,87,152,47,37,42,32,27,282,217,192,77,102,127,291,314,256,167,11,270,182,207,52,315,230,117,92,142,297,377,352,342,337,362,332,367,347,357,372,136,95,251,302,71,186,276,9,225,160,300,66,196,246,286,131,1,105,220,155,16,262,170,211,55,305,238,121,80,145,21,267,175,201,60,303,242,111,85,150,45,35,40,31,25,281,215,191,76,100,126,292,301,255,165,12,272,181,206,51,304,233,116,91,141,296,376,350,340,336,360,331,366,346,356,370 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#494ba0deb454b14b2cb7bbc62844432905ec783aba817e90b87a28e07ff9818c, M = {66} 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 23:23:22 · history