Equation 677 Database

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Magma f8fe52e01274…

magma f8fe52e01274
Size
399
Isomorphism class hash
f8fe52e01274487e7c33a8bc4dd8e8aa582e5e07cd4de4a8dfc64f50a2804537
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 06:09:37
Display reorder
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,398,90,73,54,91,55,74,92,56,75,93,57,76,94,58,77,95,59,78,96,60,79,97,61,80,98,62,72,82,63,99,83,64,100,84,65,101,85,66,102,86,67,103,87,68,104,88,69,105,89,70,106,81,71,107,51,52,53,45,46,47,48,49,50,44,36,37,39,40,41,42,43,38,389,385,383,397,171,161,207,172,208,153,173,209,154,174,210,155,175,211,156,176,212,157,177,213,158,178,214,159,179,215,160,145,200,164,146,201,165,147,202,166,148,203,167,149,204,168,150,205,169,151,206,170,152,198,162,144,199,163,186,187,188,180,181,182,183,184,185,195,196,197,190,191,192,193,194,189,384,395,396,382,113,223,0,114,2,224,115,3,216,116,4,217,108,5,218,109,6,219,110,7,220,111,8,221,112,1,222,232,10,122,233,11,123,225,12,124,226,13,125,227,14,117,228,15,118,229,16,119,230,17,120,231,9,121,135,136,137,138,139,140,141,142,143,128,129,130,132,133,134,126,127,131,388,386,390,387,261,244,297,262,298,245,263,299,246,264,300,247,265,301,248,266,302,249,267,303,250,268,304,251,269,305,243,237,290,254,238,291,255,239,292,256,240,293,257,241,294,258,242,295,259,234,296,260,235,288,252,236,289,253,278,270,271,272,273,274,275,276,277,287,279,280,282,283,284,285,286,281,392,393,391,394,338,321,372,339,373,322,340,374,323,341,375,315,333,376,316,334,377,317,335,369,318,336,370,319,337,371,320,314,365,331,306,366,332,307,367,324,308,368,325,309,360,326,310,361,327,311,362,328,312,363,329,313,364,330,344,345,346,347,348,349,350,342,343,353,354,355,357,358,359,351,352,356,379,380,378,381 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#510b34f9e6a1c6e0496dead3f3bacd7befe67e173634f2e86264f097fc4b355b, 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 06:09:39 · history