Equation 677 Database

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Magma d59e4677fbe4…

magma d59e4677fbe4
Size
321
Isomorphism class hash
d59e4677fbe400502b8763f2b7946c620b4b1824a42d0f9400f11f6fd16b38a5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:22:56
Display reorder
300,68,134,119,107,130,117,132,66,105,131,67,118,106,129,133,137,71,115,103,126,135,69,116,104,127,136,70,114,102,128,140,63,98,110,121,138,64,96,108,122,139,65,97,109,120,113,62,143,101,124,60,141,99,111,125,61,142,100,112,123,303,306,315,312,162,262,263,261,260,254,253,163,252,255,164,258,256,259,257,273,165,274,272,275,264,166,266,265,267,268,167,270,269,271,284,160,285,286,287,277,161,276,278,279,280,159,281,282,283,298,156,296,297,299,157,289,288,290,291,158,293,292,294,295,317,320,318,319,21,6,74,194,29,72,7,22,192,27,23,73,193,28,8,9,20,77,197,25,10,18,75,195,26,11,19,76,196,24,4,12,200,80,35,5,13,198,78,33,3,14,199,79,34,83,15,1,203,31,16,0,201,81,32,17,2,202,82,30,316,301,302,311,84,242,39,148,206,40,240,85,149,204,86,41,147,205,241,245,87,38,144,209,243,88,36,145,207,244,89,37,146,208,248,90,154,45,212,246,91,155,46,210,247,92,153,47,211,44,93,251,150,215,94,249,151,42,213,95,250,152,43,214,309,310,307,314,53,182,230,220,172,228,180,51,221,173,52,229,219,171,181,185,49,233,216,168,183,50,231,217,169,184,48,232,218,170,188,59,226,236,178,186,57,227,234,179,187,58,225,235,177,239,55,191,222,174,56,189,223,237,175,54,190,224,238,176,304,308,305,313 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 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#2ab683a2f54af56adf82381d164449f2b2adaada784a6acf8eff870c9ce46309, M = {60} 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 2026-10-01 22:22:57 · history