Equation 677 Database

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Magma ced65e669c61…

magma ced65e669c61
Size
381
Isomorphism class hash
ced65e669c612a268e86843cb7dbd7257720f44947dcf2eade66b5c11fd1590b
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 23:30:58
Display reorder
380,270,260,170,181,322,320,31,25,246,221,8,11,120,125,115,111,100,80,95,86,155,130,206,195,52,57,67,276,251,255,161,166,176,186,323,321,319,318,36,41,286,20,241,236,226,231,72,9,282,10,106,76,90,266,145,150,135,141,210,200,215,190,47,62,292,295,351,369,336,355,341,331,345,376,362,371,272,262,172,182,308,309,32,27,247,223,15,12,122,127,117,112,102,82,97,87,157,132,207,197,53,58,68,277,252,257,162,167,177,187,306,307,311,310,37,42,287,22,242,237,228,232,73,14,283,13,107,77,92,267,147,152,137,142,212,202,217,192,48,63,293,297,352,365,337,357,342,332,347,377,363,372,274,264,174,184,328,326,34,29,249,220,19,16,124,129,119,114,104,84,99,89,159,134,209,199,54,59,69,279,254,259,164,169,179,189,329,327,325,324,39,44,289,24,244,239,225,234,74,18,284,17,109,79,94,269,149,154,139,144,214,204,219,194,49,64,294,299,354,368,339,359,343,334,349,379,364,374,271,261,171,180,301,304,30,26,245,222,5,6,121,126,116,110,101,81,96,85,156,131,205,196,51,56,65,275,250,256,160,165,175,185,300,302,303,305,35,40,285,21,240,235,227,230,71,4,281,7,105,75,91,265,146,151,136,140,211,201,216,191,46,60,290,296,350,367,335,356,340,330,346,375,360,370,273,263,173,183,312,316,33,28,248,224,3,0,123,128,118,113,103,83,98,88,158,133,208,198,50,55,66,278,253,258,163,168,178,188,313,314,315,317,38,43,288,23,243,238,229,233,70,2,280,1,108,78,93,268,148,153,138,143,213,203,218,193,45,61,291,298,353,366,338,358,344,333,348,378,361,373 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 = {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 23:30:59 · history