Equation 677 Database

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Magma 372cb403a532…

magma 372cb403a532
Size
399
Isomorphism class hash
372cb403a5327fe95e90d08f8975f48b165d4fd36798752902882814711ad1a1
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
2026-10-07 08:41:50
Display reorder
238,239,240,241,242,234,235,236,237,247,248,249,250,251,243,244,245,246,381,252,23,233,14,15,253,24,225,254,16,25,226,255,17,26,227,18,256,9,228,257,10,19,229,258,11,20,230,259,12,21,231,260,13,22,232,261,32,7,217,262,33,8,218,263,34,1,219,264,35,0,220,265,27,2,221,266,28,3,222,267,29,4,223,268,30,5,224,269,31,6,216,392,386,385,391,214,297,333,137,138,215,298,334,207,139,299,335,208,140,300,336,301,209,141,337,210,142,302,338,211,143,303,339,212,135,304,340,213,136,305,341,198,290,130,326,199,291,131,327,200,292,132,328,201,293,133,329,202,294,134,330,203,295,126,331,204,296,127,332,205,288,128,324,206,289,129,325,384,390,389,383,306,281,150,120,121,307,282,151,308,122,283,152,309,123,284,144,285,310,124,145,311,125,286,146,312,117,287,147,313,118,279,148,314,119,280,149,315,274,113,159,316,275,114,160,317,276,115,161,318,277,116,153,319,278,108,154,320,270,109,155,321,271,110,156,322,272,111,157,323,273,112,158,387,398,397,388,105,349,342,188,180,106,351,344,107,181,353,346,99,182,355,348,357,100,183,350,101,184,359,352,102,185,343,354,103,186,345,356,104,187,347,358,98,367,197,360,90,369,189,362,91,371,190,364,92,373,191,366,93,375,192,368,94,376,193,370,95,361,194,372,96,363,195,374,97,365,196,377,393,395,396,394,77,47,68,173,174,78,48,69,79,175,49,70,80,176,50,71,51,72,177,63,73,178,52,64,74,179,53,65,75,171,45,66,76,172,46,67,86,40,166,61,87,41,167,62,88,42,168,54,89,43,169,55,81,44,170,56,82,36,162,57,83,37,163,58,84,38,164,59,85,39,165,60,380,382,379,378 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#f07132d1b231f8d7b1b263e233ceb5cbf651212a6483cd57935aa8d19f4de20a, 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 2026-10-07 08:41:51 · history