Equation 677 Database

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Magma adeee007ff0e…

magma adeee007ff0e
Size
381
Isomorphism class hash
adeee007ff0efe6df77fbfc79f3690f8a07b11d53174a6cdcc464c6edf9a664c
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 23:29:33
Display reorder
380,55,54,227,6,7,56,121,125,115,106,111,100,301,300,302,303,304,305,141,130,136,155,145,151,51,52,222,49,50,53,61,57,58,59,60,232,161,166,171,175,180,186,85,92,96,76,81,295,271,277,267,285,290,280,192,202,197,217,207,212,248,240,235,255,260,250,337,360,350,347,375,367,332,355,342,370,70,69,229,67,71,68,123,128,118,108,113,103,307,308,306,310,311,309,143,133,138,158,148,153,64,65,224,66,62,63,1,0,74,72,73,234,163,168,173,178,183,188,87,93,98,78,83,298,273,278,268,288,293,283,194,204,199,219,209,214,249,244,239,259,264,254,339,363,354,349,378,368,334,358,344,373,48,15,226,12,13,14,124,129,119,109,114,104,317,315,316,314,312,313,144,134,139,159,149,154,40,41,220,37,38,39,16,17,18,19,20,230,164,169,174,179,184,189,88,94,99,79,84,299,274,279,269,289,294,284,190,200,195,215,206,211,246,242,236,256,261,252,335,364,353,345,379,365,330,359,341,374,47,46,225,43,44,45,122,127,117,107,112,102,327,328,329,324,325,326,142,132,137,157,147,152,3,2,221,42,4,5,11,9,10,8,21,231,162,167,172,177,182,187,86,90,97,77,82,297,272,275,265,287,292,282,191,201,196,216,205,210,245,241,237,257,262,251,336,362,352,346,377,369,331,357,340,372,27,28,228,31,29,30,120,126,116,105,110,101,320,318,319,323,321,322,140,131,135,156,146,150,22,23,223,24,25,26,36,34,35,33,32,233,160,165,170,176,181,185,89,91,95,75,80,296,270,276,266,286,291,281,193,203,198,218,208,213,247,243,238,258,263,253,338,361,351,348,376,366,333,356,343,371 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {67} 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 23:29:34 · history