Equation 677 Database

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Magma 71a58d70fe55…

magma 71a58d70fe55
Size
381
Isomorphism class hash
71a58d70fe5510a1a5cff73568c3feb55a34c8363162816ed2f3ded11ea4766c
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 23:47:01
Display reorder
380,327,329,328,326,324,232,237,227,217,222,131,136,126,146,150,325,287,141,161,166,155,176,181,170,261,266,276,246,251,257,195,186,190,211,201,206,9,8,293,113,118,123,93,283,88,108,97,100,42,43,297,39,40,41,14,12,13,240,15,16,36,35,34,272,38,37,331,337,361,347,343,355,375,366,353,370,306,308,307,311,309,234,239,229,219,224,134,139,129,149,154,310,289,144,164,169,159,179,184,174,264,269,279,249,254,259,199,189,194,214,204,209,68,69,294,114,119,124,94,284,89,109,98,104,77,78,299,75,79,76,82,83,84,244,80,81,72,71,70,274,74,73,334,339,364,349,344,358,379,369,354,374,302,300,301,304,305,231,236,225,216,221,130,135,128,145,151,303,286,140,163,168,158,178,183,173,263,268,278,245,253,255,198,188,193,213,203,208,66,67,292,112,117,122,92,282,87,107,96,103,28,29,295,11,10,44,47,45,46,242,48,49,4,3,2,271,0,1,333,335,363,346,342,356,376,368,352,373,315,317,316,314,312,233,238,228,218,223,132,137,125,147,152,313,288,142,162,167,157,177,182,172,262,267,277,248,252,258,197,187,192,212,202,207,30,31,291,110,115,121,90,281,85,106,99,101,59,60,298,56,57,58,62,63,61,243,65,64,53,52,51,273,55,54,332,338,362,348,341,357,378,367,351,371,323,322,321,319,320,230,235,226,215,220,133,138,127,148,153,318,285,143,160,165,156,175,180,171,260,265,275,247,250,256,196,185,191,210,200,205,32,33,290,111,116,120,91,280,86,105,95,102,18,19,296,21,22,20,5,6,7,241,17,50,23,25,24,270,26,27,330,336,360,345,340,359,377,365,350,372 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, 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 23:47:01 · history