Equation 677 Database

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Magma 3ca6ce654687…

magma 3ca6ce654687
Size
399
Isomorphism class hash
3ca6ce6546874c3aa506536eaefa4eb8f5a434c879d7fad7a7a25937d2426ef2
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 13:08:31
Display reorder
302,303,304,305,297,298,299,300,301,294,295,296,288,289,290,291,292,293,380,230,308,271,327,328,231,309,272,329,232,310,273,330,233,311,274,331,225,312,275,332,226,313,276,324,227,314,277,325,228,306,278,326,229,307,270,336,222,317,280,337,223,318,281,338,224,319,282,339,216,320,283,340,217,321,284,322,341,218,285,333,219,323,286,334,220,315,287,335,221,316,279,391,385,386,392,259,213,76,177,178,260,214,77,179,252,215,78,171,253,207,79,172,254,208,80,173,255,209,72,174,256,210,73,175,257,211,74,176,258,212,75,169,268,205,85,170,269,206,86,162,261,198,87,163,262,199,88,164,263,200,89,201,165,264,81,166,265,202,82,167,266,203,83,168,267,204,84,383,389,390,384,196,159,111,139,140,197,160,112,141,189,161,113,142,190,153,114,143,191,154,115,135,192,155,116,136,193,156,108,137,194,157,109,138,195,158,110,131,188,151,120,132,180,152,121,133,181,144,122,134,182,145,123,126,183,146,124,147,127,184,125,128,185,148,117,129,186,149,118,130,187,150,119,388,398,397,387,243,95,343,349,351,244,96,345,353,245,97,346,355,246,98,348,357,247,90,350,359,248,91,352,342,249,92,354,344,250,93,356,347,251,94,358,367,235,104,361,369,236,105,363,371,237,106,364,373,238,107,366,375,239,99,368,100,377,240,370,360,241,101,372,362,242,102,374,365,234,103,376,394,395,396,393,55,47,10,28,29,56,48,11,30,57,49,12,31,58,50,13,32,59,51,14,33,60,52,15,34,61,53,16,35,62,45,17,27,54,46,9,20,64,39,2,21,65,40,3,22,66,41,4,23,67,42,5,24,68,43,6,44,25,69,7,26,70,36,8,18,71,37,1,19,63,38,0,378,381,379,382 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#4f88670da65119527ddb5ba349a16b4a09a12aedfa3667de845e6802909281d5, 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 13:08:35 · history