Equation 677 Database

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Magma 9fde93f18a6c…

magma 9fde93f18a6c
Size
399
Isomorphism class hash
9fde93f18a6cd13aa8a42c9a5e6eef5c1949d4a74b87e8c149c12c34c32a4d7b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 00:21:39
Display reorder
315,316,317,318,319,320,321,322,323,308,309,310,311,312,313,314,306,307,381,91,327,89,297,92,328,298,81,93,329,299,82,94,330,300,83,95,331,301,84,96,332,302,85,97,324,303,86,98,325,304,87,90,326,305,88,290,336,100,73,291,337,101,74,102,292,338,75,293,339,103,76,294,340,104,77,295,341,105,78,296,333,106,79,288,334,107,80,289,335,99,72,391,385,386,392,284,193,68,233,285,194,225,69,286,195,226,70,287,196,227,71,279,197,228,63,280,189,229,64,281,190,230,65,282,191,231,66,283,192,232,67,217,186,277,61,218,187,278,62,270,219,188,54,220,180,271,55,221,181,272,56,222,182,273,57,223,183,274,58,224,184,275,59,216,185,276,60,383,389,390,384,235,52,120,127,236,53,128,121,237,45,129,122,238,46,130,123,239,47,131,124,240,48,132,125,241,49,133,117,242,50,134,118,234,51,126,119,136,36,244,113,137,37,245,114,246,138,38,115,139,39,247,116,140,40,248,108,141,41,249,109,142,42,250,110,143,43,251,111,135,44,243,112,388,398,397,387,201,349,342,175,202,351,176,344,203,352,177,346,204,354,178,348,205,356,179,350,206,358,171,353,198,343,172,355,199,345,173,357,200,347,174,359,168,366,210,360,169,368,211,362,212,170,370,364,162,372,213,367,163,374,214,369,164,376,215,371,165,361,207,373,166,363,208,375,167,365,209,377,394,395,396,393,1,150,254,22,0,151,23,255,2,152,24,256,3,144,25,257,4,145,26,258,5,146,18,259,6,147,19,260,7,148,20,252,8,149,21,253,31,159,9,263,32,160,10,264,11,33,161,265,34,153,12,266,35,154,13,267,27,155,14,268,28,156,15,269,29,157,16,261,30,158,17,262,382,378,380,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 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#1fe368d7eb5482f4db71e976fb2202974a05b229f114f13fc72f42cc645f0731, M = the submagma generated by {0} (19 elements) 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: 21.

last edited by qawbecrdtey at 2026-10-08 00:21:40 · history