Equation 677 Database

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Magma 6aa1362846fa…

magma 6aa1362846fa
Size
399
Isomorphism class hash
6aa1362846fa75d588a640de65f0600fdd822ca3235e9d1f2e0d0efe8898befc
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 19:29:13
Display reorder
313,314,306,307,308,309,310,311,312,322,323,315,316,317,318,319,320,321,381,277,327,55,298,278,328,56,299,270,329,57,300,271,330,58,301,272,331,59,302,273,332,60,303,274,324,61,304,275,325,62,305,276,326,54,297,286,336,64,291,287,337,65,292,279,338,66,293,280,339,67,294,281,340,68,295,282,341,69,296,283,333,70,288,284,334,71,289,285,335,63,290,391,385,386,392,165,101,259,184,166,102,260,185,167,103,252,186,168,104,253,187,169,105,254,188,170,106,255,180,162,107,256,181,163,99,257,182,164,100,258,183,174,94,268,193,175,95,269,194,176,96,261,195,177,97,262,196,178,98,263,197,179,90,264,189,171,91,265,190,172,92,266,191,173,93,267,192,383,389,390,384,12,214,115,83,13,215,116,84,14,207,108,85,15,208,109,86,16,209,110,87,17,210,111,88,9,211,112,89,10,212,113,81,11,213,114,82,5,198,124,76,6,199,125,77,7,200,117,78,8,201,118,79,1,202,119,80,0,203,120,72,2,204,121,73,3,205,122,74,4,206,123,75,388,398,397,387,242,348,152,342,234,350,144,345,235,352,145,347,236,354,146,349,237,357,147,351,238,359,148,353,239,343,149,355,240,344,150,356,241,346,151,358,251,366,161,361,243,368,153,363,244,371,154,365,245,373,155,367,246,375,156,369,247,377,157,370,248,360,158,372,249,362,159,374,250,364,160,376,394,395,396,393,136,21,37,229,137,22,38,230,138,23,39,231,139,24,40,232,140,25,41,233,141,26,42,225,142,18,43,226,143,19,44,227,135,20,36,228,129,30,46,222,130,31,47,223,131,32,48,224,132,33,49,216,133,34,50,217,134,35,51,218,126,27,52,219,127,28,53,220,128,29,45,221,382,378,380,379 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#e306e8a59b07cdf4d9d24cfd9884bee32ac4071376d180d67a0f5ad89ff4197b, 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 19:29:14 · history