Equation 677 Database

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Magma 6478c0db6205…

magma 6478c0db6205
Size
381
Isomorphism class hash
6478c0db6205852396ae3540776a00e820494671feb3fc713961a289ffc3e6a0
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 23:32:28
Display reorder
380,145,123,143,293,144,142,206,180,185,190,196,201,260,265,270,275,281,286,121,122,117,118,119,120,132,133,134,135,130,131,301,300,302,303,304,305,295,220,225,211,216,2,245,250,255,231,235,240,176,150,155,160,166,171,141,136,137,138,139,140,125,124,126,127,128,129,350,360,346,344,337,356,343,365,376,370,83,82,84,290,80,81,208,183,189,194,199,204,263,268,274,279,284,289,57,58,59,60,61,56,73,68,69,70,71,72,329,324,325,326,327,328,298,224,229,214,218,148,248,253,259,233,238,243,178,153,159,164,169,174,76,77,78,79,74,75,66,65,67,62,63,64,353,363,349,342,335,358,334,368,378,373,4,3,5,294,146,6,205,181,186,191,195,200,261,266,271,276,280,285,30,25,26,27,28,29,17,18,13,14,15,16,307,308,309,310,311,306,296,221,226,210,215,116,246,251,256,230,236,241,175,151,156,161,165,170,20,21,22,23,24,19,10,9,11,12,7,8,351,361,345,339,336,355,340,366,377,371,102,101,103,292,99,100,209,184,188,193,198,203,264,269,273,278,283,288,105,106,107,108,109,104,92,87,88,89,90,91,318,319,320,321,322,323,299,223,228,213,219,149,249,254,258,234,239,244,179,154,158,163,168,173,95,96,97,98,93,94,114,113,115,110,111,112,354,364,348,333,331,359,330,369,379,374,0,49,1,291,85,86,207,182,187,192,197,202,262,267,272,277,282,287,54,55,50,51,52,53,37,38,39,40,41,42,317,312,313,314,315,316,297,222,227,212,217,147,247,252,257,232,237,242,177,152,157,162,167,172,46,47,48,43,44,45,36,35,31,32,33,34,352,362,347,341,332,357,338,367,375,372 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {74} 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 23:32:29 · history