Equation 677 Database

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Magma 56f24da53c64…

magma 56f24da53c64
Size
399
Isomorphism class hash
56f24da53c64b96691e5be60cfb8b6ea8da9796d4fba3ce1e18ac72f2c0da9e0
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
2026-10-06 21:09:19
Display reorder
252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,381,308,327,285,302,309,328,286,303,329,310,287,304,330,311,279,305,312,331,280,297,313,281,298,332,314,324,282,299,306,325,283,300,307,326,284,301,278,336,317,295,318,270,337,296,271,338,319,288,272,339,320,289,273,340,321,290,274,341,322,291,275,333,323,292,276,334,315,293,277,335,316,294,391,385,386,392,19,187,4,132,20,188,5,133,180,21,6,134,181,22,7,126,23,182,8,127,24,1,128,183,25,184,0,129,26,185,2,130,18,186,3,131,13,196,28,141,29,14,197,142,15,189,30,143,16,190,31,135,17,191,32,136,9,192,33,137,10,193,34,138,11,194,35,139,12,195,27,140,383,389,390,384,198,84,233,96,199,85,225,97,86,200,226,98,87,201,227,90,202,88,228,91,203,229,92,89,204,81,230,93,205,82,231,94,206,83,232,95,217,77,207,105,208,218,78,106,219,79,209,107,220,80,210,99,221,72,211,100,222,73,212,101,223,74,213,102,224,75,214,103,216,76,215,104,388,398,397,387,69,349,172,342,70,351,173,344,352,71,174,346,354,63,175,348,64,356,176,350,65,177,353,358,66,343,178,355,67,345,179,357,68,347,171,359,165,367,62,360,54,166,369,362,167,370,55,364,168,372,56,366,169,374,57,368,170,376,58,371,162,361,59,373,163,363,60,375,164,365,61,377,394,395,396,393,119,248,41,161,120,249,42,153,250,121,43,154,251,122,44,155,123,243,36,156,124,37,157,244,125,245,38,158,117,246,39,159,118,247,40,160,50,241,112,145,113,51,242,146,52,234,114,147,53,235,115,148,45,236,116,149,46,237,108,150,47,238,109,151,48,239,110,152,49,240,111,144,382,379,380,378 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#42902ea010f3b3f11daefc1532fc40b68a9dff17fd024f11feee7d9760ad7ce2, 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 2026-10-06 21:09:21 · history