Equation 677 Database

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Magma 865dc4a6b7a2…

magma 865dc4a6b7a2
Size
336
Isomorphism class hash
865dc4a6b7a2da6f5da9fda174347ff4d2266026c4478719746603b3b6265b4f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 335) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 08:10:26
Display reorder
103,104,105,91,92,93,94,95,96,97,98,99,100,101,102,317,249,286,280,250,203,177,13,204,178,14,205,179,15,206,180,16,207,181,12,208,276,247,287,277,17,197,182,18,198,183,19,199,184,20,200,185,21,201,186,22,285,278,279,248,202,43,35,36,37,38,39,40,41,42,44,34,294,295,296,297,328,326,315,334,300,291,308,301,1,164,72,2,165,73,3,166,74,4,167,75,5,168,76,6,169,77,7,170,78,8,171,79,292,309,299,293,172,68,9,173,69,10,174,70,11,175,176,71,0,209,212,213,214,215,216,217,218,219,230,232,234,210,211,229,322,331,329,316,160,62,29,161,63,30,162,64,252,275,258,253,152,57,31,153,274,254,271,259,32,154,65,33,155,66,23,156,67,24,157,58,25,158,59,26,272,257,251,273,60,27,28,159,61,88,80,81,82,83,84,85,86,87,89,90,305,302,303,304,319,333,321,330,306,310,298,307,187,50,150,188,51,151,189,52,270,281,255,268,190,53,144,191,54,145,192,55,143,193,56,163,282,256,269,283,45,146,194,46,147,195,47,148,196,48,49,149,284,290,288,289,221,222,223,224,225,226,228,231,233,235,220,227,323,327,332,325,123,140,108,124,141,109,125,142,110,126,131,111,127,132,112,128,133,113,129,134,114,130,135,115,262,265,260,263,266,261,264,267,116,119,136,117,120,137,118,121,138,106,107,122,139,237,238,239,240,241,242,243,244,245,246,236,313,314,312,311,324,318,320,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 336 = 16 + 5*64, 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 58, 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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 2026-10-08 08:10:29 · history