Equation 677 Database

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Magma 4eb1f8f403d2…

magma 4eb1f8f403d2
Size
399
Isomorphism class hash
4eb1f8f403d2e89c623c7b57e91cc3973471fb0dbd4ffd18d95c22b899ba98bb
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 10:11:41
Display reorder
211,212,213,214,215,207,208,209,210,204,205,206,198,199,200,201,202,203,381,168,156,218,188,169,219,157,180,170,220,158,181,162,221,159,182,163,222,160,183,164,223,161,184,165,224,153,185,166,216,154,186,167,217,155,187,177,149,227,197,150,178,228,189,151,179,229,190,152,171,230,191,144,172,231,192,173,145,232,193,174,146,233,194,147,175,225,195,176,148,226,196,392,386,385,391,142,299,253,333,143,254,300,334,135,255,301,335,136,256,302,336,137,257,303,337,138,258,304,338,139,259,305,339,140,260,297,340,141,252,298,341,126,292,262,326,293,127,263,327,294,128,264,328,295,129,265,329,296,130,266,330,131,288,267,331,132,289,268,332,290,133,269,324,134,291,261,325,384,390,389,383,85,243,306,281,86,307,244,282,87,308,245,283,88,309,246,284,89,310,247,285,81,311,248,286,82,312,249,287,83,313,250,279,84,314,251,280,78,236,315,274,237,79,316,275,238,80,317,276,239,72,318,277,240,73,319,278,74,241,320,270,75,242,321,271,234,76,322,272,77,235,323,273,387,398,397,388,63,349,116,342,64,108,351,344,65,109,353,346,66,110,355,348,67,111,357,350,68,112,359,352,69,113,343,354,70,114,345,356,71,115,347,358,56,367,125,360,369,57,117,362,371,58,118,364,373,59,119,366,375,60,120,368,61,376,121,370,62,361,122,372,363,54,123,374,55,365,124,377,393,395,396,394,102,2,51,19,103,52,3,20,104,53,4,21,105,45,5,22,106,46,6,23,107,47,7,24,99,48,8,25,100,49,1,26,101,50,0,18,95,11,44,28,12,96,36,29,13,97,37,30,14,98,38,31,15,90,39,32,91,16,40,33,92,17,41,34,9,93,42,35,94,10,43,27,380,382,379,378 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#2a50a45e23513a31a23c3402437f17ceb6be8a5911f0d2b6606f3e3034a2f3cf, 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 10:11:42 · history