Equation 677 Database

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Magma 454b995cd4e2…

magma 454b995cd4e2
Size
381
Isomorphism class hash
454b995cd4e278c9ed2262496d68acaa10c3ec85005f5ff7c14da2848cdf6d22
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:44:37
Display reorder
380,45,44,46,47,48,43,228,229,230,231,226,227,41,42,37,38,39,40,285,291,296,270,275,280,29,30,25,26,27,28,235,232,233,1,239,234,260,265,241,245,250,255,193,194,195,190,191,192,303,304,305,301,300,302,31,36,197,198,199,32,33,200,34,201,35,196,362,340,368,338,337,369,363,372,339,376,87,86,88,237,84,85,213,208,209,210,211,212,94,89,90,91,92,93,286,290,295,271,276,281,171,166,167,168,169,170,202,203,204,205,206,207,261,266,240,246,251,256,138,139,140,141,142,137,316,313,314,312,329,315,177,176,134,135,136,172,173,131,174,132,175,133,353,332,364,359,358,365,352,370,330,377,14,13,15,16,17,18,183,178,179,180,181,182,22,23,24,19,20,21,288,293,298,273,278,283,238,151,152,153,149,150,188,189,184,185,186,187,263,268,243,248,253,258,61,62,63,64,65,66,306,307,308,309,310,311,145,144,72,67,68,146,147,69,148,70,143,71,343,336,360,354,355,361,344,374,335,378,73,78,74,75,76,77,163,164,165,160,161,162,79,80,81,82,83,236,287,292,297,272,277,282,222,223,224,225,220,221,156,157,158,159,154,155,262,267,242,247,252,257,57,58,59,60,55,56,321,322,317,318,319,320,216,215,54,49,50,217,218,51,219,52,214,53,341,331,357,366,367,356,342,371,345,375,106,105,101,102,103,104,0,2,3,4,5,6,98,99,100,95,96,97,289,294,299,274,279,284,127,128,129,130,125,126,8,9,10,11,12,7,264,269,244,249,254,259,109,110,111,112,107,108,324,325,326,327,328,323,121,120,115,116,117,122,123,118,124,113,119,114,348,347,333,350,351,334,349,373,346,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {69} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:44:38 · history