Equation 677 Database

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Magma 6ee298e4b6d8…

magma 6ee298e4b6d8
Size
381
Isomorphism class hash
6ee298e4b6d855e4843e50cc2cf5dd8d18d216d87552b254b10d9ef49373a95d
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 23:31:02
Display reorder
380,304,302,208,218,105,96,244,238,56,77,150,161,115,120,125,136,141,5,20,11,52,26,271,261,191,180,176,305,301,300,198,203,213,223,110,100,92,87,248,253,228,233,67,61,82,72,155,145,165,280,131,0,16,303,42,47,31,37,276,266,291,255,186,171,286,296,373,330,345,377,357,353,341,336,361,366,313,317,209,219,109,99,241,239,59,79,154,164,119,124,129,139,144,9,24,14,54,29,274,264,194,184,179,314,315,316,199,204,214,224,114,104,94,89,249,254,229,234,69,64,84,74,159,149,169,284,134,4,18,312,44,49,34,39,279,269,294,259,189,174,289,299,374,334,348,379,359,354,344,339,364,369,309,307,205,215,108,98,242,235,58,78,153,163,118,123,128,138,143,8,23,13,53,28,273,263,193,183,178,310,308,306,196,200,211,221,113,103,93,88,246,251,225,230,68,63,83,73,158,148,168,283,133,3,17,311,43,48,33,38,278,268,293,258,188,173,288,298,371,333,347,378,358,351,343,337,363,368,318,322,206,216,107,97,240,236,55,76,151,160,116,121,126,135,140,6,21,12,51,25,270,260,190,181,175,319,323,321,195,201,210,220,111,101,91,86,245,250,226,231,65,60,81,71,156,146,166,281,130,1,19,320,41,46,30,35,275,265,290,256,185,170,285,295,370,331,346,375,356,350,340,338,360,365,326,327,207,217,106,95,243,237,57,75,152,162,117,122,127,137,142,7,22,10,50,27,272,262,192,182,177,324,328,329,197,202,212,222,112,102,90,85,247,252,227,232,66,62,80,70,157,147,167,282,132,2,15,325,40,45,32,36,277,267,292,257,187,172,287,297,372,332,349,376,355,352,342,335,362,367 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, 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 23:31:03 · history