Equation 677 Database

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Magma 2b6a3a44acf8…

magma 2b6a3a44acf8
Size
396
Isomorphism class hash
2b6a3a44acf89c6cc6f2215dd7e511ca1ae4ebacb02cc387cb298cdf6da831a7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 05:46:29
Display reorder
394,366,317,352,307,57,318,114,4,58,77,115,5,59,78,116,6,60,79,117,7,61,80,327,308,314,319,328,8,51,81,107,9,52,82,108,10,53,83,109,11,54,84,110,1,85,55,111,0,320,315,329,306,316,56,112,2,76,50,113,3,94,86,87,88,89,90,91,92,93,322,95,323,324,321,356,385,390,383,386,331,140,247,240,121,141,248,241,122,142,249,242,123,143,250,243,124,144,251,244,125,145,252,363,358,335,253,234,126,146,254,235,127,147,343,341,353,367,344,342,332,148,255,236,149,118,256,237,150,330,364,362,151,119,245,238,152,120,246,239,181,187,188,189,190,191,192,193,180,182,183,184,185,186,338,379,381,393,388,373,355,360,195,281,67,209,196,282,68,210,197,283,69,211,198,280,70,212,199,287,71,213,200,288,72,214,201,290,73,215,202,292,74,216,203,294,75,217,204,296,62,218,205,63,298,219,206,64,300,220,207,65,302,221,208,66,304,222,194,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,376,375,377,357,339,347,165,104,223,266,166,105,224,267,167,106,225,257,153,325,340,365,154,96,226,258,155,97,227,259,156,98,228,260,157,99,229,261,158,351,368,345,159,100,230,262,160,231,101,263,161,232,102,264,162,233,103,265,163,361,326,346,164,168,172,173,174,175,176,177,178,179,169,170,171,336,337,359,384,380,391,387,372,309,350,49,268,18,27,37,269,19,28,38,270,20,29,39,271,21,30,40,272,22,31,41,273,23,32,42,274,24,33,43,275,12,310,312,348,354,311,313,349,13,34,44,14,276,35,45,15,277,36,46,16,278,26,47,17,279,25,48,128,135,136,137,138,139,129,130,131,132,133,134,333,334,371,378,389,382,392 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#7c9587bb487c7f78877b32bd3c6516b6b04394ef6d405ed5492c6ed5480f025c, M = {75} 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, 79): MacNeish's product over GF(79); 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 2026-10-02 05:46:31 · history